Maths-
General
Easy

Question

Tell whether the given sequence is an arithmetic sequence. 15,13,11,9,....

Hint:

  • A sequence is said to be arithmetic if the common difference is always constant.
  • The General formula of any AP is a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d.

The correct answer is: ⇒-2


    Explanation:
    • We have given a sequence 15,13,11,9,...
    • We have to find weather the given sequence is AP or not.
    Step 1 of 1:
    We have given sequence 15,13,11,9,...
    The difference in first two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 13 minus 15 end cell row cell not stretchy rightwards double arrow negative 2 end cell end table
    Now the difference in next two terms is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 11 minus 13 end cell row cell not stretchy rightwards double arrow negative 2 end cell end table
    Since the difference is constant
    The given sequence is arithmetic sequence.

    Related Questions to study

    General
    Maths-

    Write an explicit formula for the arithmetic sequence.
    an = 12 - 5n

    • We have given an explicit formula an = 12 - 5n
    • We have to find the recursive formula
    Step 1 of 1:
    We have given a explicit formula an = 12 - 5n

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript 1 equals 12 minus 5 end cell row cell a subscript 1 equals 7 end cell end table
    Now,

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n minus 1 end subscript equals 12 minus 5 left parenthesis n minus 1 right parenthesis end cell row cell a subscript n minus 1 end subscript equals 12 minus 5 n plus 5 end cell row cell a subscript n minus 1 end subscript equals a subscript n plus 5 end cell end table
    So, The recursive formula is a subscript n minus 1 end subscript equals a subscript n plus 5.

    Write an explicit formula for the arithmetic sequence.
    an = 12 - 5n

    Maths-General
    • We have given an explicit formula an = 12 - 5n
    • We have to find the recursive formula
    Step 1 of 1:
    We have given a explicit formula an = 12 - 5n

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript 1 equals 12 minus 5 end cell row cell a subscript 1 equals 7 end cell end table
    Now,

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n minus 1 end subscript equals 12 minus 5 left parenthesis n minus 1 right parenthesis end cell row cell a subscript n minus 1 end subscript equals 12 minus 5 n plus 5 end cell row cell a subscript n minus 1 end subscript equals a subscript n plus 5 end cell end table
    So, The recursive formula is a subscript n minus 1 end subscript equals a subscript n plus 5.

    General
    Maths-

    Write an explicit formula for the arithmetic sequence.
    an = 8 + 3n

    • We have given an explicit formula an = 8 + 3n
    • We have to find the recursive formula
    Step 1 of 1:
    We have given a explicit formula an = 8 + 3n
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript 1 equals 8 plus 3 end cell row cell a subscript 1 equals 11 end cell end table
    Now,

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n minus 1 end subscript equals 8 plus 3 left parenthesis n minus 1 right parenthesis end cell row cell a subscript n minus 1 end subscript equals 8 plus 3 n minus 3 end cell row cell a subscript n minus 1 end subscript equals a subscript n minus 3 end cell end table
    So, The recursive formula is a subscript n minus 1 end subscript equals a subscript n minus 3.

    Write an explicit formula for the arithmetic sequence.
    an = 8 + 3n

    Maths-General
    • We have given an explicit formula an = 8 + 3n
    • We have to find the recursive formula
    Step 1 of 1:
    We have given a explicit formula an = 8 + 3n
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript 1 equals 8 plus 3 end cell row cell a subscript 1 equals 11 end cell end table
    Now,

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n minus 1 end subscript equals 8 plus 3 left parenthesis n minus 1 right parenthesis end cell row cell a subscript n minus 1 end subscript equals 8 plus 3 n minus 3 end cell row cell a subscript n minus 1 end subscript equals a subscript n minus 3 end cell end table
    So, The recursive formula is a subscript n minus 1 end subscript equals a subscript n minus 3.

    General
    Maths-

    Use long Division to rewrite each rational function. Find the asymptotes of  and sketch the graph.
    straight F left parenthesis straight x right parenthesis equals fraction numerator x over denominator x minus 6 end fraction

    1.Find the asymptotes of the rational function, if any.
    2.Draw the asymptotes as dotted lines.
    3.Find the 
    x -intercept (s) and y -intercept of the rational function, if any.
    4.Find the values of y for several different values of x .
    5.Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
    x - 6= 0
    x = 6
    The vertical asymptote of the rational function is x= 6
    We will find more points on the function and graph the function.


    From the graph we can analyze that the vertical asymptote of the rational function is  x= 6 and horizontal asymptote is
    y = (leading coefficient of numerator) / (leading coefficient of denominator) = 1 over 1=1

    Use long Division to rewrite each rational function. Find the asymptotes of  and sketch the graph.
    straight F left parenthesis straight x right parenthesis equals fraction numerator x over denominator x minus 6 end fraction

    Maths-General
    1.Find the asymptotes of the rational function, if any.
    2.Draw the asymptotes as dotted lines.
    3.Find the x -intercept (s) and y -intercept of the rational function, if any.
    4.Find the values of y for several different values of x .
    5.Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
    x - 6= 0
    x = 6
    The vertical asymptote of the rational function is x= 6
    We will find more points on the function and graph the function.


    From the graph we can analyze that the vertical asymptote of the rational function is  x= 6 and horizontal asymptote is
    y = (leading coefficient of numerator) / (leading coefficient of denominator) = 1 over 1=1
    parallel
    General
    Maths-

    Write an explicit formula for the arithmetic sequence.
    a subscript n equals a subscript n minus 1 end subscript plus 2.4 semicolon a subscript 1 equals negative 1

    • We have given a subscript n equals a subscript n minus 1 end subscript plus 2.4 and a subscript 1 equals negative 1
    • We have to find the explicit formula for this AP.
    Step 1 of 1:
    We know that the common difference d is also equal to d equals a subscript n minus a subscript n minus 1 end subscript
    Now in given question we have a subscript n equals a subscript n minus 1 end subscript plus 2.4
    Ie,
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n minus a subscript n minus 1 end subscript equals 2.4 end cell row cell d equals 2.4 end cell end table

    And a1 = -1
    So, The explicit formula will be
    a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals negative 1 plus left parenthesis n minus 1 right parenthesis left parenthesis 2.4 right parenthesis end cell row cell a subscript n equals negative 1 plus 2.4 n minus 2.4 end cell row cell a subscript n equals 2.4 n minus 3.4 end cell end table

    Write an explicit formula for the arithmetic sequence.
    a subscript n equals a subscript n minus 1 end subscript plus 2.4 semicolon a subscript 1 equals negative 1

    Maths-General
    • We have given a subscript n equals a subscript n minus 1 end subscript plus 2.4 and a subscript 1 equals negative 1
    • We have to find the explicit formula for this AP.
    Step 1 of 1:
    We know that the common difference d is also equal to d equals a subscript n minus a subscript n minus 1 end subscript
    Now in given question we have a subscript n equals a subscript n minus 1 end subscript plus 2.4
    Ie,
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n minus a subscript n minus 1 end subscript equals 2.4 end cell row cell d equals 2.4 end cell end table

    And a1 = -1
    So, The explicit formula will be
    a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals negative 1 plus left parenthesis n minus 1 right parenthesis left parenthesis 2.4 right parenthesis end cell row cell a subscript n equals negative 1 plus 2.4 n minus 2.4 end cell row cell a subscript n equals 2.4 n minus 3.4 end cell end table

    General
    Maths-

    Write an explicit formula for the arithmetic sequence. a subscript n equals a subscript n minus 1 end subscript minus 3 semicolon a subscript 1 equals 10

    • We have given an = an - 1 - 3 and a1 = 10
    • We have to find the explicit formula for this AP.
    Step 1 of 1:
    We know that the common difference d is also equal to d equals a subscript n minus a subscript n minus 1 end subscript
    Now in given question we have a subscript n equals a subscript n minus 1 end subscript minus 3
    Ie,

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n minus a subscript n minus 1 end subscript equals negative 3 end cell row cell d equals negative 3 end cell end table

    And a1 = 10
    So, The explicit formula will be
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d end cell row cell a subscript n equals 10 plus left parenthesis n minus 1 right parenthesis left parenthesis negative 3 right parenthesis end cell row cell a subscript n equals 10 minus 3 n plus 3 end cell row cell a subscript n equals 13 minus 3 n end cell end table

    Write an explicit formula for the arithmetic sequence. a subscript n equals a subscript n minus 1 end subscript minus 3 semicolon a subscript 1 equals 10

    Maths-General
    • We have given an = an - 1 - 3 and a1 = 10
    • We have to find the explicit formula for this AP.
    Step 1 of 1:
    We know that the common difference d is also equal to d equals a subscript n minus a subscript n minus 1 end subscript
    Now in given question we have a subscript n equals a subscript n minus 1 end subscript minus 3
    Ie,

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n minus a subscript n minus 1 end subscript equals negative 3 end cell row cell d equals negative 3 end cell end table

    And a1 = 10
    So, The explicit formula will be
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d end cell row cell a subscript n equals 10 plus left parenthesis n minus 1 right parenthesis left parenthesis negative 3 right parenthesis end cell row cell a subscript n equals 10 minus 3 n plus 3 end cell row cell a subscript n equals 13 minus 3 n end cell end table

    General
    Maths-

    Use long Division to rewrite each rational function. Find the asymptotes of  and sketch the graph.
    straight F left parenthesis straight x right parenthesis equals fraction numerator 6 x over denominator 2 x plus 1 end fraction

    1.Find the asymptotes of the rational function, if any.
    2.Draw the asymptotes as dotted lines.
    3.Find the 
    x -intercept (s) and y -intercept of the rational function, if any.
    4.Find the values of y for several different values of x .
    5.Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
    2x + 1= 0
    x = fraction numerator negative 1 over denominator 2 end fraction
    The vertical asymptote of the rational function is x =fraction numerator negative 1 over denominator 2 end fraction
    We will find more points on the function and graph the function.



    From the graph we can analyze that the vertical asymptote of the rational function is  x= fraction numerator negative 1 over denominator 2 end fraction and horizontal asymptote is
    y = (leading coefficient of numerator) / (leading coefficient of denominator) = 6 over 2=3

    Use long Division to rewrite each rational function. Find the asymptotes of  and sketch the graph.
    straight F left parenthesis straight x right parenthesis equals fraction numerator 6 x over denominator 2 x plus 1 end fraction

    Maths-General
    1.Find the asymptotes of the rational function, if any.
    2.Draw the asymptotes as dotted lines.
    3.Find the x -intercept (s) and y -intercept of the rational function, if any.
    4.Find the values of y for several different values of x .
    5.Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
    2x + 1= 0
    x = fraction numerator negative 1 over denominator 2 end fraction
    The vertical asymptote of the rational function is x =fraction numerator negative 1 over denominator 2 end fraction
    We will find more points on the function and graph the function.



    From the graph we can analyze that the vertical asymptote of the rational function is  x= fraction numerator negative 1 over denominator 2 end fraction and horizontal asymptote is
    y = (leading coefficient of numerator) / (leading coefficient of denominator) = 6 over 2=3
    parallel
    General
    Maths-

    The cost to rent a bike is $28 for the first day plus $2 for each day after that. Write an explicit formula for the rental cost for n days. What is the cost of renting a bike for 8 days?

    • We have given a cost of rent of bike $28 for the first day plus$2 for each day after that.
    • We have to write an explicit formula for the rental cost for n days and cost of renting bike for 8 days.
    Step 1 of 2:
    We have given first day cost is $28 and for each more day $2 will be charged
    Here

    a1 = 28

    d = 2
    We know that general formula is an = a1 + (n - 1)d
    So,
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d end cell row cell a subscript n equals 28 plus left parenthesis n minus 1 right parenthesis 2 end cell row cell a subscript n equals 28 plus 2 n minus 2 end cell row cell a subscript n equals 2 n plus 26 end cell end table
    Step 2 of 2:
    Now, Cost of renting for 8 days will be
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals 2 n plus 26 end cell row cell a subscript 8 equals 2 left parenthesis 8 right parenthesis plus 26 end cell row cell a subscript 8 equals 16 plus 26 end cell row cell a subscript 8 equals 42 end cell end table

    The cost to rent a bike is $28 for the first day plus $2 for each day after that. Write an explicit formula for the rental cost for n days. What is the cost of renting a bike for 8 days?

    Maths-General
    • We have given a cost of rent of bike $28 for the first day plus$2 for each day after that.
    • We have to write an explicit formula for the rental cost for n days and cost of renting bike for 8 days.
    Step 1 of 2:
    We have given first day cost is $28 and for each more day $2 will be charged
    Here

    a1 = 28

    d = 2
    We know that general formula is an = a1 + (n - 1)d
    So,
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d end cell row cell a subscript n equals 28 plus left parenthesis n minus 1 right parenthesis 2 end cell row cell a subscript n equals 28 plus 2 n minus 2 end cell row cell a subscript n equals 2 n plus 26 end cell end table
    Step 2 of 2:
    Now, Cost of renting for 8 days will be
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals 2 n plus 26 end cell row cell a subscript 8 equals 2 left parenthesis 8 right parenthesis plus 26 end cell row cell a subscript 8 equals 16 plus 26 end cell row cell a subscript 8 equals 42 end cell end table

    General
    Maths-

    The daily attendance at an amusement park after day x is given by the function
    f(x) =fraction numerator 3.000 x over denominator x squared minus 1 end fraction.      On Approximately which day will the attendance be 1125 people ?

    We have given the equation of the daily attendance at an amusement park after day x
    F(x) =  F left parenthesis x right parenthesis equals fraction numerator 3.000 x over denominator x squared minus 1 end fraction
    We have to find on which day attendance will be 1125
    y = f(x) = 1125
    1125 equals fraction numerator 3.000 x over denominator x squared minus 1 end fraction
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 1125 over 3 equals fraction numerator x over denominator x squared minus 1 end fraction end cell row blank end table
    375 equals fraction numerator x over denominator x squared minus 1 end fraction
    375 x squared plus x minus 375 equals 0                   
    x = -1.001   or x= 0.999

    The daily attendance at an amusement park after day x is given by the function
    f(x) =fraction numerator 3.000 x over denominator x squared minus 1 end fraction.      On Approximately which day will the attendance be 1125 people ?

    Maths-General
    We have given the equation of the daily attendance at an amusement park after day x
    F(x) =  F left parenthesis x right parenthesis equals fraction numerator 3.000 x over denominator x squared minus 1 end fraction
    We have to find on which day attendance will be 1125
    y = f(x) = 1125
    1125 equals fraction numerator 3.000 x over denominator x squared minus 1 end fraction
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 1125 over 3 equals fraction numerator x over denominator x squared minus 1 end fraction end cell row blank end table
    375 equals fraction numerator x over denominator x squared minus 1 end fraction
    375 x squared plus x minus 375 equals 0                   
    x = -1.001   or x= 0.999
    General
    Maths-

    Graph each function and identify the horizontal and vertical asymptotes
    straight F left parenthesis straight x right parenthesis equals fraction numerator 3 x squared minus 11 x minus 4 over denominator 4 x squared minus 25 end fraction

    1. Find the asymptotes of the rational function, if any.
    2. Draw the asymptotes as dotted lines.
    3. Find the x -intercept (s) and y -intercept of the rational function, if any.
    4. Find the values of y for several different values of x .
    5. Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
    4x2 -25 = 0
    4x2 = 25
    x2 = 25 over 4
    x =5 over 2  and    x = fraction numerator negative 5 over denominator 2 end fraction
    The vertical asymptote of the rational function is x=−1.
    This function has no x -intercept at (4,0) and y -intercept at (0,7) . We will find more points on the function and graph the function.



    From the graph we can analyze that the vertical asymptote of the rational function is  x= fraction numerator negative 5 over denominator 2 end fraction and horizontal asymptote is
    y = (leading coefficient of numerator) / (leading coefficient of denominator) = 3 over 4= 0.75.

    Graph each function and identify the horizontal and vertical asymptotes
    straight F left parenthesis straight x right parenthesis equals fraction numerator 3 x squared minus 11 x minus 4 over denominator 4 x squared minus 25 end fraction

    Maths-General
    1. Find the asymptotes of the rational function, if any.
    2. Draw the asymptotes as dotted lines.
    3. Find the x -intercept (s) and y -intercept of the rational function, if any.
    4. Find the values of y for several different values of x .
    5. Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
    4x2 -25 = 0
    4x2 = 25
    x2 = 25 over 4
    x =5 over 2  and    x = fraction numerator negative 5 over denominator 2 end fraction
    The vertical asymptote of the rational function is x=−1.
    This function has no x -intercept at (4,0) and y -intercept at (0,7) . We will find more points on the function and graph the function.



    From the graph we can analyze that the vertical asymptote of the rational function is  x= fraction numerator negative 5 over denominator 2 end fraction and horizontal asymptote is
    y = (leading coefficient of numerator) / (leading coefficient of denominator) = 3 over 4= 0.75.
    parallel
    General
    Maths-

    Graph each function and identify the horizontal and vertical asymptotes
    r left parenthesis x right parenthesis equals fraction numerator 2 x squared plus 7 over denominator 1 plus 2 x plus x end fraction 2

    1. Find the asymptotes of the rational function, if any.
    2. Draw the asymptotes as dotted lines.
    3. Find the x -intercept (s) and y -intercept of the rational function, if any.
    4. Find the values of y for several different values of x .
    5. Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
    x2 + 2x + 1= 0
    x2 +x + x + 1= 0
    x(x + 1) + 1 (x + 1) = 0
    (x + 1) (x + 1) = 0
    x + 1 = 0   or    x + 1 = 0
    x = -1
    The vertical asymptote of the rational function is x=−1.
    This function has no x -intercept  and y -intercept at (0,7) . We will find more points on the function and graph the function.




    From the graph we can analyze that the vertical asymptote of the rational function is  x = -1  and degree of the numerator is greater than the denominator, then there is no horizontal asymptote.

    Graph each function and identify the horizontal and vertical asymptotes
    r left parenthesis x right parenthesis equals fraction numerator 2 x squared plus 7 over denominator 1 plus 2 x plus x end fraction 2

    Maths-General
    1. Find the asymptotes of the rational function, if any.
    2. Draw the asymptotes as dotted lines.
    3. Find the x -intercept (s) and y -intercept of the rational function, if any.
    4. Find the values of y for several different values of x .
    5. Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
    x2 + 2x + 1= 0
    x2 +x + x + 1= 0
    x(x + 1) + 1 (x + 1) = 0
    (x + 1) (x + 1) = 0
    x + 1 = 0   or    x + 1 = 0
    x = -1
    The vertical asymptote of the rational function is x=−1.
    This function has no x -intercept  and y -intercept at (0,7) . We will find more points on the function and graph the function.




    From the graph we can analyze that the vertical asymptote of the rational function is  x = -1  and degree of the numerator is greater than the denominator, then there is no horizontal asymptote.
    General
    Maths-

    Write an equation of the line that passes through the point (4, 5) and is perpendicular to the graph of y = 2x + 3

    • We have to write an equation of the line that passes through the point (4, 5) and is perpendicular to the graph of 𝑦 = 2𝑥 + 3.
    Step 1 of 1:
    We have to find a line passes through a point (4, 5) and perpendicular to a line 𝑦 = 2𝑥 + 3.
    Since product of two perpendicular lines is equal to -1.
    So,

     m cross times 2 equals negative 1

    m equals fraction numerator negative 1 over denominator 2 end fraction
    Therefore the equation of the line will be

     y minus 5 equals fraction numerator negative 1 over denominator 2 end fraction left parenthesis x minus 4 right parenthesis

    y equals fraction numerator negative 1 over denominator 2 end fraction x plus 7

    Write an equation of the line that passes through the point (4, 5) and is perpendicular to the graph of y = 2x + 3

    Maths-General
    • We have to write an equation of the line that passes through the point (4, 5) and is perpendicular to the graph of 𝑦 = 2𝑥 + 3.
    Step 1 of 1:
    We have to find a line passes through a point (4, 5) and perpendicular to a line 𝑦 = 2𝑥 + 3.
    Since product of two perpendicular lines is equal to -1.
    So,

     m cross times 2 equals negative 1

    m equals fraction numerator negative 1 over denominator 2 end fraction
    Therefore the equation of the line will be

     y minus 5 equals fraction numerator negative 1 over denominator 2 end fraction left parenthesis x minus 4 right parenthesis

    y equals fraction numerator negative 1 over denominator 2 end fraction x plus 7

    General
    Maths-

    Graph each function and identify the horizontal and vertical asymptotes
    straight F left parenthesis straight x right parenthesis equals fraction numerator 3 over denominator x minus 2 end fraction

    1. Find the asymptotes of the rational function, if any.
    2. Draw the asymptotes as dotted lines.
    3. Find the x -intercept (s) and y -intercept of the rational function, if any.
    4. Find the values of y for several different values of x .
    5. Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
    x – 2 = 0
    x = 2
    The vertical asymptote of the rational function is x= 2.
    This function has no x -intercept and has y -intercept at (0,-1.5) . We will find more points on the function and graph the function


    From the graph we can analyze that the vertical asymptote of the rational function is  x= 2  and horizontal asymptote is y = 0

    Graph each function and identify the horizontal and vertical asymptotes
    straight F left parenthesis straight x right parenthesis equals fraction numerator 3 over denominator x minus 2 end fraction

    Maths-General
    1. Find the asymptotes of the rational function, if any.
    2. Draw the asymptotes as dotted lines.
    3. Find the x -intercept (s) and y -intercept of the rational function, if any.
    4. Find the values of y for several different values of x .
    5. Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
    x – 2 = 0
    x = 2
    The vertical asymptote of the rational function is x= 2.
    This function has no x -intercept and has y -intercept at (0,-1.5) . We will find more points on the function and graph the function


    From the graph we can analyze that the vertical asymptote of the rational function is  x= 2  and horizontal asymptote is y = 0
    parallel
    General
    Maths-

    Graph each function and identify the horizontal and vertical asymptotes
    straight F left parenthesis straight x right parenthesis equals to the power of x 2 minus 1

    1. Find the asymptotes of the rational function, if any.
    2. Draw the asymptotes as dotted lines.
    3. Find the x -intercept (s) and y -intercept of the rational function, if any.
    4. Find the values of y for several different values of x .
    5. Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
    x2 - 1= 0
    x = 1   or   x = -1
    The vertical asymptote of the rational function is x=−1 and x= 1  .
    This function has the x -intercept at (−14,0) and y -intercept at (0,4.167) . We will find more points on the function and graph the function.


    From the graph we can analyze that the vertical asymptote of the rational function is x =−1 and x = 1  and horizontal asymptote is y = 0

    Graph each function and identify the horizontal and vertical asymptotes
    straight F left parenthesis straight x right parenthesis equals to the power of x 2 minus 1

    Maths-General
    1. Find the asymptotes of the rational function, if any.
    2. Draw the asymptotes as dotted lines.
    3. Find the x -intercept (s) and y -intercept of the rational function, if any.
    4. Find the values of y for several different values of x .
    5. Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
    The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
    x2 - 1= 0
    x = 1   or   x = -1
    The vertical asymptote of the rational function is x=−1 and x= 1  .
    This function has the x -intercept at (−14,0) and y -intercept at (0,4.167) . We will find more points on the function and graph the function.


    From the graph we can analyze that the vertical asymptote of the rational function is x =−1 and x = 1  and horizontal asymptote is y = 0
    General
    Maths-

    Write an equation of the line in slope-intercept form that passes through the point (-3, 5)  and is parallel to y equals negative 2 over 3 x
.

    • We have been given in the question two points for which we have to write an equation of the line in slope-intercept form that passes through the point (-3, 5) and is parallel to y equals negative 2 over 3 x
    Step 1 of 1:
    We have to find a line passes through a point (-3, 5) and parallel to a line y equals negative 2 over 3 x
    Since two parallel lines have same slope.
    So, Slope of the line will be fraction numerator negative 2 over denominator 3 end fraction
    Therefore the equation of the line will be

    y minus 5 equals fraction numerator negative 2 over denominator 3 end fraction left parenthesis x plus 3 right parenthesis

    y equals fraction numerator negative 2 over denominator 3 end fraction x plus 3.

    Write an equation of the line in slope-intercept form that passes through the point (-3, 5)  and is parallel to y equals negative 2 over 3 x
.

    Maths-General
    • We have been given in the question two points for which we have to write an equation of the line in slope-intercept form that passes through the point (-3, 5) and is parallel to y equals negative 2 over 3 x
    Step 1 of 1:
    We have to find a line passes through a point (-3, 5) and parallel to a line y equals negative 2 over 3 x
    Since two parallel lines have same slope.
    So, Slope of the line will be fraction numerator negative 2 over denominator 3 end fraction
    Therefore the equation of the line will be

    y minus 5 equals fraction numerator negative 2 over denominator 3 end fraction left parenthesis x plus 3 right parenthesis

    y equals fraction numerator negative 2 over denominator 3 end fraction x plus 3.

    General
    Maths-

    What is the graph of f(x