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 - Page 203: 53

Answer

$\text{Domain: } (-\infty,\infty) \\\text{Range: } (-\infty,\infty)$
1513993075

Work Step by Step

$\bf{\text{Solution Outline:}}$ To graph the given linear function, $ f(x)=-2x+5 ,$ find two points on the line by identifying the $y$-intercept and the slope. Use the geometric interpretation of slope as $\dfrac{rise}{run}.$ Then use the graph to identify the domain and range of the function. $\bf{\text{Solution Details:}}$ A linear function in the form $f(x)=mx+b,$ has a $y$-intercept of $b$ and a slope of $m.$ Since the $y$-intercept is $ 5 ,$ the graph passes through $( 0,5 ).$ With a slope of $m= -2=\dfrac{-2}{1} =\dfrac{rise}{run} ,$ then from the $y$-intercept, move $ 2 $ units down and then $ 1 $ unit to the right to get the point $( 1,3 ).$ Based on the graph the domain and range are as follows: \begin{array}{l}\require{cancel} \text{Domain: } (-\infty,\infty) \\\text{Range: } (-\infty,\infty) .\end{array}
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