Q. 14 - 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 graphs of $y=3^x$ and  $y={\left(\frac{1}{3}\right)}^x$ are identical.

Step-by-Step Solution

Answer

False. The graph of $y=3^x$ and $y={\left(\frac{1}{3}\right)}^x$ are not identical.

Step 1. Given

The function $$\begin{gathered} y=3^x, \\ y={\left(\frac{1}{3}\right)}^x \end{gathered}$$ are identical.

Step 2. Comparing two functions

The function $$\begin{gathered} y={\left(\frac{1}{3}\right)}^x \\ =3^{-x} \end{gathered}$$ 

is not identical since $y={\left(\frac{1}{3}\right)}^x$ is is a reflection about the $y-$axis of the
graph of $y=3^x$.

So they are not identical.