# Asymptotes of rational function

Given: y = (x+1)(x-5)/[( x-3)(x+2)]

1. Where are the zeros of y? Draw them on a piece of graph paper, or write "none".

2. Where are the vertical asymptotes? Draw them on your graph, or write "none".

3. Where are the horizontal asymptotes? Draw them on your graph, or write "none".

4. Where are the slant asymptotes? Draw them on your graph, or write "none".

5. What is y(6)?

6. What is y(-4)?

7. Sketch the shape of the expected function of y on your graph paper. Remember, your plot must go through the points in (5) and (6) plus any zeroes without crossing any asymptotes

https://brainmass.com/math/basic-algebra/asymptotes-rational-function-612810

#### Solution Preview

Given: y = (x+1)(x-5)/[( x-3)(x+2)]

1. Where are the zeros of y? Draw them on a piece of graph paper, or write "none".

Solution:

To find the zeros of y, put (x+1)(x-5)/[( x-3)(x+2)] = 0

(x+1)(x-5)/[( x-3)(x+2)] = 0

(x+1)(x-5) = 0

x = -1, 5

2. Where are the vertical asymptotes? Draw them on ...

#### Solution Summary

This solution explains how to graph a rational function by finding vertical asymptotes, horizontal asymptotes and zeros of the function.