Chapter 5.2, Problem 9E

Solution

To graph: The function $g\left(x\right)=\frac{-6}{x}$ and compare the graph with $y=\frac{1}{x}$.

Given information:

The function $g\left(x\right)=\frac{-6}{x}$ and the parent function is $y=\frac{1}{x}$.

Graph:

The given function is in form of $f\left(x\right)=\frac{a}{x}$ and its parent function is $y=\frac{1}{x}$.

The asymptotes of the parent function will be $x=0,y=0$ and its domain and range will be the set of real numbers except $0$.

The function in the form of $f\left(x\right)=\frac{a}{x}$ will have same asymptote, domain and range as that of the parent function.

Make a table to find some points on the graph that are to the left and right of the vertical asymptote.

$x$	$-3$	$-2$	$2$	$3$
$y=\frac{-6}{x}$	$2$	$3$	$-3$	$-2$

Draw the graph of the given function and the parent function.

  

Interpretation:

Both functions lie in different quadrants but they have same asymptotes, domain and range. The graph of $g\left(x\right)=\frac{-6}{x}$ is farther from the axes as compared to the graph of the parent function.