Maths-
General
Easy
Question
What is the graph of the function![f left parenthesis x right parenthesis equals fraction numerator 2 x plus 1 over denominator 3 x minus 4 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGYAAAAjCAYAAABmSn+9AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAu5JREFUeNrtWztoFFEUfQQJQdKIiIVIIASRFGEhhYRFgiAisoUELMRCgiAiQdJZiYXNkiIEsRELCwtBRESCCCIiIQRBRERE0liJncUWsoTAei57imHy5u377EzGmXfgkOz8Mrtn3v2cvVGqWmiCz8EOuAN+Aa+U6P5OgHd4X7XCB/AyOM7X0+Amt5UBT8DrYE9FqAnwa07X7hV8XuXQ1Wy7BrY12+9xXxQmZ8wxnOnwGTyaeL0IPogrJn+MgR9ZFOhwHlzl72fBdzGU5Y9D4Evw3IDj3oLzrJQOW3yggxiFMWCSokxZHLvM0nomJv98cRJ8BB506HtWPUvq0ghzM6OSMaHN84qAJPJn4AHLVfWKAkrf88kilO27MCOpakVxqW95Xm/TM1S4Yp0rZhCOgK9TQrTYAJZWGKlU/pDfEk+ffLgNzxuZBTcKEMYmKY+CL8BjmvOf8v0XeX9WEBF+JQSY5s+GoRewxQYFivDAAp+aNFbApcBr3/LITxHEXfC2Zvsb8HSgrTHn0cBFMO4mY1+yfOwwNofYGqO8Tp6NW2XxAzyu2b47oFiwtTV24vPvVyL/zdi3OyRbIw9hehXjHpwC32e8eVMos7U1YijzhOSUx4YV0Qy0NWLy98R91f/aUzmUyy62xhKvE+FRlV3I2KdrMF1tjdhgekIsmDHD/q1EDnG1NYqyZCoHefp/DzjmfzAxz3AVS3Up3/Nvg2vK3TXOGy2bgmaN/YuNXXLDw1ZZMeSuYUOqyoVUBdmgc1EWSC7+biPMLN9MldEp0b08VH27qvZuxiQjQhrDGF9yRTPRMtRWGPHvFplnsqrN0PElF0h4lcHDiboKk3YMlg3Hho4vuaCd6gVru2JkfOmi6s+VzRuOK2J8aUbTB9Y+x4xTnCyEjC/ZQv7+VBRmL7qGZBwyvuQbXqNBy5WwnVGthY4vhYpVG8j/x1xS/aGSEToBP8GrGqdjGONLURhLyFzCOkNXl05AS1O27tf4krUw/wA+oR1XunwmuQAAAPF0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+ZjwvbWk+PG1vPig8L21vPjxtaT54PC9taT48bW8+KTwvbW8+PG1vPj08L21vPjxtZnJhYz48bXJvdz48bW4+MjwvbW4+PG1pPng8L21pPjxtbz4rPC9tbz48bW4+MTwvbW4+PC9tcm93Pjxtcm93Pjxtbj4zPC9tbj48bWk+eDwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bW4+NDwvbW4+PC9tcm93PjwvbWZyYWM+PC9tYXRoPgcjCvUAAAAASUVORK5CYII=)
Hint:
A rational function is a function that is the ratio of polynomials. Any function of one variable, x, is called a rational function if, it can be represented as f(x) =
, where p(x) and q(x) are polynomials such that q(x) ≠ 0.
Rational functions are of the form y = f(x)y = fx , where f(x)fx is a rational expression .
- If both the polynomials have the same degree, divide the coefficients of the leading terms. This is your asymptote.
- If the degree of the numerator is less than the denominator, then the asymptote is located at y = 0 (which is the x-axis).
- If the degree of the numerator is greater than the denominator, then there is no horizontal asymptote.
The correct answer is: From the graph we can analyze that the vertical asymptote of the rational function is x= 4/3. and horizontal asymptote is y = (leading coefficient of numerator) / (leading coefficient of denominator) = 2/3
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 .
3x - 4= 0
3x = 4
x = ![4 over 3](data:image/png;base64,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)
The vertical asymptote of the rational function is x=![4 over 3](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAMlJREFUeNpjYCAO+ADxfwYKAQ8QX6OGQTOBOJlSg6yBeC+UTbZBbEB8CYjlKTWoA4hzkPhkGaQHxEfRxMgy6CQQq1DDoP8EMEWAYgMGr0GjgIrgP5l4FAwW4AjE24D4GxD/AOJbQDwBiIVJNWg/EAdBy20YMADiHdRy6SdqGKIExDcoMUAciBOh4eRFjSxTQKmXBIE4AFqz2FMjjHighlEF/KCGIXrQACcJHATiUCBmAWImaEq/D8TxpBpkC8RboF75AU3pPvg0AADVaEDn8baWUAAAAGJ0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1uPjQ8L21uPjxtbj4zPC9tbj48L21mcmFjPjwvbWF0aD6enGumAAAAAElFTkSuQmCC)
We will find more points on the function and graph the function.
![](data:image/png;base64,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)
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)
From the graph we can analyze that the vertical asymptote of the rational function is x=
. and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) = ![2 over 3](data:image/png;base64,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)
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What are the vertical and horizontal asymptotes of the graph of each function?
![fraction numerator x squared plus 5 x plus 4 over denominator 3 x squared minus 12 end fraction](data:image/png;base64,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)
What are the vertical and horizontal asymptotes of the graph of each function?
![fraction numerator x squared plus 5 x plus 4 over denominator 3 x squared minus 12 end fraction](data:image/png;base64,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)
Maths-General
Maths-
The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is parallel to the north path.
The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is parallel to the north path.
Maths-General
Maths-
Write recursive formula and explicit formula. 12,19,26,33,40,...
Write recursive formula and explicit formula. 12,19,26,33,40,...
Maths-General
Maths-
What are the vertical and horizontal asymptotes of the graph of each function?
![G left parenthesis x right parenthesis equals fraction numerator 2 x squared plus x minus 9 over denominator x squared minus 2 x minus 8 end fraction](data:image/png;base64,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)
What are the vertical and horizontal asymptotes of the graph of each function?
![G left parenthesis x right parenthesis equals fraction numerator 2 x squared plus x minus 9 over denominator x squared minus 2 x minus 8 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Are graphs of the equations parallel, perpendicular or neither?
![y equals negative 5 x space straight & space 25 x plus 5 y equals 1](data:image/png;base64,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)
Are graphs of the equations parallel, perpendicular or neither?
![y equals negative 5 x space straight & space 25 x plus 5 y equals 1](data:image/png;base64,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)
Maths-General
Maths-
Tell whether the given sequence is an arithmetic sequence. 93,86,79,72,66,...
Tell whether the given sequence is an arithmetic sequence. 93,86,79,72,66,...
Maths-General
Maths-
Are graphs of the equations parallel, perpendicular or neither?
![y equals 2 x plus 6 space straight & space y equals 1 half x plus 3](data:image/png;base64,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)
Are graphs of the equations parallel, perpendicular or neither?
![y equals 2 x plus 6 space straight & space y equals 1 half x plus 3](data:image/png;base64,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)
Maths-General
Maths-
Tell whether the given sequence is an arithmetic sequence. 37,3,31,29,26,23,...
Tell whether the given sequence is an arithmetic sequence. 37,3,31,29,26,23,...
Maths-General
Maths-
What are the horizontal asymptotes for the graph
![f left parenthesis x right parenthesis equals fraction numerator 3 x minus 2 over denominator x squared plus 7 x plus 12 end fraction](data:image/png;base64,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)
What are the horizontal asymptotes for the graph
![f left parenthesis x right parenthesis equals fraction numerator 3 x minus 2 over denominator x squared plus 7 x plus 12 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Tell whether the given sequence is an arithmetic sequence. 3,6,9,15,18,...
Tell whether the given sequence is an arithmetic sequence. 3,6,9,15,18,...
Maths-General
Maths-
Tell whether the given sequence is an arithmetic sequence. 3,6,9,12,15,18,...
Tell whether the given sequence is an arithmetic sequence. 3,6,9,12,15,18,...
Maths-General