Chapter 12, Problem 1MCP

To determine

To graph the given function and give its domain and range.

Answer to Problem 1MCP

Solution:

The graph for the function $f\left(x\right)=2^x-3$

is shown below:

Domain of the function $f\left(x\right)=2^x-3$ is: $\left(-\infty ,\infty \right)$

Range of the function $f\left(x\right)=2^x-3$ is: $\left(-3,\infty \right)$

Explanation of Solution

Given:

The function: $f\left(x\right)=2^x-3$ .

Calculation:

Let us consider some of the points to plot the graph of the function $f\left(x\right)=2^x-3$ .

$x$	$f\left(x\right)$
$-4$	$-2.9375$
$-2$	$-2.75$
$0$	$-2$
$2$	$1$
$4$	$13$

Joining the points above in the table by freehand, we get the graph of the function $f\left(x\right)=2^x-3$ .

Since, the function $f\left(x\right)=2^x-3$ is defined for all the values of $x$ .

Therefore, the domain of the function $f\left(x\right)=2^x-3$ is: $\left(-\infty ,\infty \right)$

Since, from the graph of the function $f\left(x\right)=2^x-3$ , the function is always greater than $-3$

Therefore, the range of the function $f\left(x\right)=2^x-3$ is: $\left(-3,\infty \right)$