Chapter 1.3, Problem 9E

To determine

To find: The zeros of the function $f\left(x\right)=2^x-5$ with the help of graph.

Answer to Problem 9E

The zeros of the function $f\left(x\right)=2^x-5$ is $x=2.322$.

Explanation of Solution

Given information:

The function is $f\left(x\right)=2^x-5$.

Calculation:

The zeros of the function are the values of $x$ where the graph of the function meets the $x$ -axis.

To graph a function $f\left(x\right)=2^x-5$ , follow the steps using graphing calculator.

First press “ON” button on graphical calculator, press $\boxed{\text{Y}=}$ key and enter right hand side of the equation $f\left(x\right)=2^x-5$ after the symbol ${\text{Y}}_1$ . Enter the keystrokes $\boxed{2}\boxed{^}\boxed{(}\boxed{\text{X}}\boxed{)}\boxed{-}\boxed{5}$.

The display will show the equation,

  ${\text{Y}}_{\text{1}}=2^{\text{X}}-5$

Now, press the $\boxed{\text{GRAPH}}$ key and $\boxed{\text{TRACE}}$ key to produce the graph of given quadratic equation in standard window as shown below.

  

Figure (1)

The graph of the function $f\left(x\right)=2^x-5$ meets the $x$ -axis at the point $\left(2.322,0\right)$.

Therefore, the zeros of the function $f\left(x\right)=2^x-5$ is $x=2.322$.