Question

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

## The correct answer is: The vertical asymptote of the rational function is x= 3 and x=-8 .We will find more points on the function and graph the function.

### 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.

Solution:-

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 }+5x - 24= 0

x^{2 }+ 8x - 3x - 24= 0

x(x+ 8)- 3(x + 8) = 0

(x- 3) (x+8)

x = 3 and x = -8

The vertical asymptote of the rational function is x= 3 and x=-8 .We will find more points on the function and graph the function.

x

y

-14

13.176

-30

7.934

-10

27.692

X

Y

4

4

12

4

3.2

10.286

From the graph we can analyze that the vertical asymptote of the rational function is x= 3 and x= -8 and horizontal asymptote is

y = (leading coefficient of numerator) / (leading coefficient of denominator) = 6/1=6

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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.

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