Question

# Graph the function, labelling all horizontal or vertical asymptotes of the form x = a or y = b

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) = p(x)/q(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: The vertical asymptote of the rational function is x= 6 and x=-3/2 .We will find more points on the function and graph the function.

### 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^{2 }-9x - 18= 0

2x^{2 }-12x + 3x - 18= 0

2x(x - 6)+ 3(x - 6) = 0

(x - 6) (2x + 3)

x = 6 and x = -3/2

The vertical asymptote of the rational function is x= 6 and x=-3/2 .We will find more points on the function and graph the function.

x

y

-2

0

-1.6

-0.684

-4

0.2

X

Y

8

1.842

6.5

5.844

13

0.887

From the graph we can analyze that the vertical asymptote of the rational function is x= 6 and x= -3/2 and horizontal asymptote is

y = (leading coefficient of numerator) / (leading coefficient of denominator) = ½=0.5

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### The graphs of and are parallel lines. What is the value of ?

When two lines have distinct y-intercepts but the same slope, they are said to be parallel. They are perpendicular if the slopes of two lines are negative reciprocals of one another.

Parallel-Line: Two or more lines present in the same plane but never crossing each other are said to be parallel lines. They don't have anything in common.

Perpendicular-Line: Perpendicular lines are two lines that meet at an intersection point, which form 4 right angles.

Slope: The slope of a line indicates how sharp it is and is calculated by dividing the distance that a point on the line must travel horizontally and vertically to reach another point. Y-Intercept: Y-Intercept is the point at which the graph crosses the y-axis. From the Given Equation, the parallel lines can be written as 3x-9y=15 and y=mx-4. If the corresponding angles are equal, the two lines are considered parallel.

### The graphs of and are parallel lines. What is the value of ?

When two lines have distinct y-intercepts but the same slope, they are said to be parallel. They are perpendicular if the slopes of two lines are negative reciprocals of one another.

Parallel-Line: Two or more lines present in the same plane but never crossing each other are said to be parallel lines. They don't have anything in common.

Perpendicular-Line: Perpendicular lines are two lines that meet at an intersection point, which form 4 right angles.

Slope: The slope of a line indicates how sharp it is and is calculated by dividing the distance that a point on the line must travel horizontally and vertically to reach another point. Y-Intercept: Y-Intercept is the point at which the graph crosses the y-axis. From the Given Equation, the parallel lines can be written as 3x-9y=15 and y=mx-4. If the corresponding angles are equal, the two lines are considered parallel.