College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.1 - Exponential Functions - 4.1 Exercises: 8

Answer

$f(\frac{1}{2})\approx 0.577$; $f(2.5) \approx. 5.196$; $f(-1)\approx 0.111$; $f(\frac{1}{4}) \approx. 0.439$

Work Step by Step

Evaluate the function for the given values of $x$ by substituting each $x$ into $f(x)$ then using a calculator to find the exact value. When x=$\frac{1}{2}$: $f(x) = 3^{x-1} \\f(1/2)=3^{\frac{1}{2}-1} \\f(1/2)=3^{-\frac{1}{2}} \\f(1/2)\approx 0.577$ When $x=2.5$: $f(x) = 3^{x-1} \\f(2.5) = 3^{2.5-1} \\f(2.5)=3^{1.5} \\f(2.5) \approx. 5.196$ When $x=-1$: $f(x)=3^{x-1} \\f(-1)=3^{-1-1} \\f(-1)=3^{-2} \\f(-1)\approx 0.111$ When $x=\frac{1}{4}$: $f(x)=3^{x-1} \\f(\frac{1}{4}) = 3^{\frac{1}{4}-1} \\f(\frac{1}{4}) = 3^{-\frac{3}{4}} \\f(\frac{1}{4}) \approx. 0.439$
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