Chapter 5.2, Problem 1GP

Solution

To graph: The function $f\left(x\right)=-\frac{4}{x}$ and state its domain and range.

Given information:

The function $f\left(x\right)=-\frac{4}{x}$.

Graph:

Draw the asymptotes $x=0,y=0$ on a coordinate plane.

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

$x$	$-4$	$-1$	$1$	$4$
$y=-\frac{4}{x}$	$1$	$4$	$-4$	$-1$

Plot the points on the coordinate plane.

Draw the branches of the hyperbola such that they pass through the points and approach the asymptotes.

  

Domain is the set of $x-$ values and range is the set of $y-$ values.

From the graph it can be observed that all real values except $0$ are in the set of $x-$ values and all real values except $0$ are in the set of $y-$ values.

Interpretation:

The domain and range of the given function is the set of all real values other than $0$.