Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 2 - Section 2.6 - Function Notation and Linear Functions - 2.6 Exercises: 48

Answer

$\text{a) } f(x)=\dfrac{1}{4}x-2 \\\\\text{b) } f(3)=-\dfrac{5}{4}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of equality to isolate $y$ in the given equation, $ x-4y=8 ,$ and then express in function notation. Then find $f(3)$ by substituting $x$ with $3.$ $\bf{\text{Solution Details:}}$ Using the properties of equality, the given equation is equivalent to \begin{array}{l}\require{cancel} x-4y=8 \\\\ -4y=-x+8 \\\\ \dfrac{-4y}{-4}=\dfrac{-x}{{-4}}+\dfrac{8}{-4} \\\\ y=\dfrac{1}{4}x-2 .\end{array} Using $y=f(x),$ the function notation of the equation above is $ f(x)=\dfrac{1}{4}x-2 .$ Substituting $x$ with $ 3 ,$ then \begin{array}{l}\require{cancel} f(x)=\dfrac{1}{4}x-2 \\\\ f(3)=\dfrac{1}{4}(3)-2 \\\\ f(3)=\dfrac{3}{4}-2 \\\\ f(3)=\dfrac{3}{4}-\dfrac{8}{4} \\\\ f(3)=-\dfrac{5}{4} .\end{array} Hence, \begin{array}{l}\require{cancel} \text{a) } f(x)=\dfrac{1}{4}x-2 \\\\\text{b) } f(3)=-\dfrac{5}{4} .\end{array}
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