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Q. 40

Expert-verified
Found in: Page 284

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

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

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

See the step by step solution

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 $\left(-1,3\right),\left(0,1\right)$, and $\left(1,\frac{1}{3}\right)$

The graph contains the points $\left(0,3\right),\left(1,1\right)$, 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 $y={3}^{-\left(x-1\right)}$

localid="1646661078860" $y={3}^{1-x}$

So it matches to (g)