College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 4 - Section 4.1 - Properties of Linear Functions and Linear Models - 4.1 Assess Your Understanding: 20


(a) Slope $= 0$ and y-intercept $=-2$ (b) See the image. (c) Average rate of change $= 0$ (d) The linear function $G(x)=-2$ is constant.

Work Step by Step

Step-1: Compare the given equation with the slope-intercept form of the linear equation, that is, $G(x) = mx+b$, where $m$ is the slope of the linear function and $b$ is its y-intercept. By comparing $$G(x)=-2$$ to $$G(x) = mx+b$$ we understand that the slope of the given function is $0$, and its y-intercept is $-2$. Note that $G(x)$ can be rewritten as $G(x) = 0\times x -2$. Step-2: Let us put values of $x$ from $-2$ to $2$ into the function to obtain corresponding $y$ values. Using this we can plot a graph. Thus, For $x=-2$, $G(x)=-2$ For $x=-1$, $G(x)=-2$ For $x=0$, $G(x)=-2$ For $x=1$, $G(x)=-2$ For $x=2$, $G(x) = -2$ This data obtains the graph shown. Step-3: The average rate of change is defined as follows: $$\frac{\Delta y}{\Delta x}=\frac{G(x_2)-G(x_1)}{x_2-x_1}$$ Let us calculate average rate of change between $x_2=2$ and $x_1=-2$, $$\frac{\Delta y}{\Delta x}=\frac{-2-(-2)}{2-(-2)}=0$$ Step-4: Since slope $=0$, this linear function is constant.
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