Answer
$f(x)=5^x.$
Work Step by Step
The graph goes through the point $(0,1)$ hence the function is in the form $f(x)=a^x.$
$(1,5)$ is on the graph, hence $f(1)=a^1=5\\a=5.$
Therefore $f(x)=5^x.$
Precalculus (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0-32197-907-9
ISBN 13:
978-0-32197-907-0
Chapter 5 - Exponential and Logarithmic Functions - 5.3 One-to-One Functions; Inverse Functions - 5.3 Assess Your Understanding - Page 282: 90
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