Q. 9 - Precalculus Enhanced with Graphing Utilities

Question

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

True or False 

The range of the exponential function $f\left(x\right)=a^x$, where $a>0$ and $a\ne 1$, is the set of all real numbers.

Step-by-Step Solution

Answer

False. The range of the exponential function is the set of all positive real numbers.

Step 1. Given

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

To find the range of the function.

Step 2. To find the range of the function.

The domain of the exponential function is the set of all real numbers and the range is the set of all positive real numbers.

So the given statement is false.