Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 11 - Cumulative Review Exercises - Page 1180: 8

Answer

See below:
1570764133

Work Step by Step

Consider the provided function, $ f\left( x \right)=\left\{ \begin{align} & -x+1\ \ \ \text{ for }-1\le x<1 \\ & 2\ \ \ \ \text{ for }x=1 \\ & {{x}^{2}}\ \ \text{ for }x>\text{1} \\ \end{align} \right.$ Here, the function is a combination of three sub-functions, $ f\left( x \right)=-x+1\text{ for }-1\le x<1$, $ f\left( x \right)=2\text{ for }x=1$ and $ f\left( x \right)={{x}^{2}}\text{ for }x>1$ Consider the first rule $ f\left( x \right)=-x+1\text{ for }-1\le x<1$, which defines a straight line. The line should be graphed only for $-1\le x<1$ -- that is, to the left of $ x=1$ and to the right of $ x=-1$ Substitute some values of x in $ f\left( x \right)=-x+1\text{ for }-1\le x<1$ Put $ x=-1$ $\begin{align} & f\left( -1 \right)=-\left( -1 \right)+1 \\ & =1+1 \\ & =2 \end{align}$ The point $\left( -1,2 \right)$ is graphed as a closed dot as the point is a part of the function. And, put $ x=1$ $\begin{align} & f\left( 1 \right)=-\left( 1 \right)+1 \\ & =-1+1 \\ & =0 \end{align}$ The point $\left( 1,0 \right)$ is graphed as open dot as the point is not the part of the function. Consider the second rule $ f\left( x \right)=2\text{ for }x=1$ which defines a single point to be plotted only for $ x=1$. Now consider the third rule $ f\left( x \right)={{x}^{2}}\text{ for }x>1$ The line should be graphed only for $ x>1$
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