## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 2 - Section 2.6 - Rational Functions and Their Graphs - Exercise Set - Page 402: 122

#### Answer

The graph is shown below:

#### Work Step by Step

Consider the functions $y=\frac{1}{x},y=\frac{1}{{{x}^{3}}},$ and $y=\frac{1}{{{x}^{5}}}$. Step 1: Write the functions $y=\frac{1}{x}$ , $y=\frac{1}{{{x}^{3}}},$ and $y=\frac{1}{{{x}^{5}}}$. Step 2: Set the window $\left( -5,5,1 \right)$ and $\left( -5,5,1 \right)$. Step 3: Plot the graph. In the graph, the slope of the function $y=\frac{1}{{{x}^{5}}}$ approaches zero faster than the other two functions $y=\frac{1}{{{x}^{3}}},y=\frac{1}{x}$. The function $y=\frac{1}{{{x}^{3}}}$ approaches zero faster than function $y=\frac{1}{x}$. In general, the graph of the function $y=\frac{1}{{{x}^{n}}}$ approaches zero faster as the n value increases. Therefore, as $x$ tends to zero, the graph of the function $y=\frac{1}{x}$ approaches infinity faster than the other two functions.

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