Chapter 3, Problem 1RE

State whether the given statement is true or false.

The function $f\left(x\right)=a^x$

is exponential if $a>0$.

To determine

To calculate:

The objective is to check whether the given statement is true or false.

“The function $f\left(x\right)=a^x$ is exponential if $a>0$ .”

Answer to Problem 1RE

The given statement “The function $f\left(x\right)=a^x$ is exponential if $a>0$ ” is false.

Explanation of Solution

Given:

The given statement is:

“The function $f\left(x\right)=a^x$ is exponential if $a>0$ .”

Calculation:

The given statement is:

“The function $f\left(x\right)=a^x$ is exponential if $a>0$ .”

An equation is in the forms of $a^x\left(a>0,a\ne 1\right)$ is known as exponential equation.

Thus, the function $f\left(x\right)=a^x$ is exponential if $a>0$ is false statement because the conditions is $a>0\text{as}a=1$.

Therefore, the given function is a constant function.

Hence, the given statement “The function $f\left(x\right)=a^x$ is exponential if $a>0$ ” is false.