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: 56

Answer

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

Work Step by Step

$\bf{\text{Solution Outline:}}$ To graph the given linear function, $ F(x)=-\dfrac{1}{4}x+1 ,$ 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 $ 1 ,$ the graph passes through $(0, 1 ).$ With a slope of $m= -\dfrac{1}{4}=\dfrac{-1}{4} =\dfrac{rise}{run} ,$ then from the $y$-intercept, move $ 1 $ unit down and then $ 4 $ units to the right to get the point $( 4,0 ).$ 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}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.