Precalculus (6th Edition)

Published by Pearson

Chapter 2 - Graphs and Functions - 2.4 Linear Functions - 2.4 Exercises - Page 228: 27

Answer

domain: $\left\{-2\right\}$ range: $\left\{-\infty, +\infty\right\}$ Refer to the graph below. The line contains the points $(-2, 0)$ and $(-2, 3)$. Plot the points above and connect them using a line. (Refer to the graph in the answer part above.)

Work Step by Step

Solve for $x$ to obtain: $2x+4=0 \\2x+4-4=0-4 \\2x=-4 \\\frac{2x}{2}=\frac{-4}{2} \\x=-2$ This means the given equation is equivalent to $x=-2$. RECALL: The line $x=a$, where $a$ is a real number:: (a) is vertical. All points on this line have an x-coordinate of $a$; (b) has the set of real numbers as its range; and (c) has a domain of $\left\{a\right\}$ Thus, the graph of the equation $x=-2$ is a vertical line. All points on the line have an x-coordinate of $-2$. The domain is $\left\{-2\right\}$. The range is $\left\{-\infty, +\infty\right\}$. The line contains the points $(-2, 0)$ and $(-2, 3)$. Plot the points above and connect them using a line. (Refer to the graph in the answer part above.)

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