Find Intercepts and Asymptotes

Practice Questions

Pre-Calculus › Find Intercepts and Asymptotes

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1

Find the zeros and asymptotes for

$y = \frac{2x^2 + 5 x - 3 }{2x^2 + 3x - 2 }$ .

2

Find the slant asymptote for

$y = \frac{2x^2 - 13 x - 7 }{ x - 7 }$ .

3

Find the slant and vertical asymptotes for the equation

$y = \frac{2x^2 - 5 x + 1 }{x + 3 }$ .

4

What is the -intercept of the following function?

$\frac{x^2 + 3x + 6}{x + 2}$

5

Which of these functions has a vertical asymptote of and a slant asymptote of ?

6

Suppose the function below has an oblique (i.e. slant asymptote) at .

$\frac{ax^n+3x+5}{bx^m+6}$

If we are given , what can we say about the relation between and and between and ?

7

Find the -intercept and asymptote, if possible.

$y=\frac{x^2+4x+3}{(x+3)}$

8

Find the y-intercept of $y=\frac{3-x}{x-3}+3$ , if any.

9

Find the y-intercept and asymptote, respectively, of the following function, if possible. $y=\frac{3x}{x}$

10

Find the horizontal asymptote of the function:

$f(x) = \frac{x^2+6x+9}{x^2+5x+6}$

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