
To graph the rational function and show the x-andy-intercepts and asymptotes.

Explanation of Solution
Given information:
The rational function is
Graph:
Factor:
x-intercepts: the x-intercept are the zeros of the numerator,
So, x-intercept is
y-intercepts: to find y-intercept, substitute
So, y-intercept is
Horizontal asymptote: the degree of numerator and denominator is same,
So the horizontal asymptote will be the division of leading coefficient of numerator and denominator,
Vertical asymptote: the vertical asymptote is occurs where denominator is zero,
So vertical asymptote is
Slant asymptote: the slant asymptote is occurs when the numerator degree is one more than denominator, using division algoritum,
Thus,
Use the above information together with some additional values which is show in table below
To sketch the graph,
x | y |
-2 | 18 |
0 | -12 |
1 | -4.5 |
2 | -2 |
Thus, the graph is obtained as:
Interpretation:
From the above graph it can be observed that the x-intercept is
Chapter 3 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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