Q. 40 - Precalculus Enhanced with Graphing Utilities

Question

In Problems $33-40$, the graph of an exponential function is given. Match each graph to one of the following functions.

Step-by-Step Solution

Answer

The function is $y=3^{1-x}$ and matches to (g)

Step 1: Given information

Given graph 

Step 2: Checking the graph and forming the function

The  graph is a reflection about the $y$-axis of $y=3^x$. Thus, an equation would be $y=3^{-x}$

The function $y=3^{-x}$, being a reflection about the $y$-axis of $y=3^x$, contains the points $(-1,3),(0,1)$, and $(1,\frac{1}{3})$

The graph contains the points $(0,3),(1,1)$, and $\left(2,\frac{1}{3}\right)$. When compared to the three points mentioned above, these points involve one -unit shift to the right.

Thus, the equation of the graph must be $y=3^{-(x-1)}$

$y=3^{1-x}$

So it matches to (g)