Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 2 - Graphs and Functions - 2.4 Linear Functions - 2.4 Exercises - Page 228: 22

Answer

domain: $(-\infty, +\infty)$ range: $(-\infty, +\infty)$
1516751152

Work Step by Step

The given line can be graphed using the x and y-intercepts. RECALL: (1) The x-intercept can be found by setting $y=0$ then solving for $x$. (2) The y-intercept can be found by setting $x=0$ then solving for $y$. Find the x-intercept of the given equation. Set $y=0$ then solve for $x$ to obtain: \begin{array}{ccc} \\&2x+5y&=&10 \\&2x+5(0)&=&10 \\&2x&=&10 \\&\frac{2x}{2}&=&\frac{10}{2} \\&x&=&5 \end{array} The x-intercept is $(5, 0)$. Find the x-intercept of the given equation. Set $x=0$ then solve for $y$ to obtain: \begin{array}{ccc} \\&2x+5y&=&10 \\&2(0)+5y&=&10 \\&5y&=&10 \\&\frac{5y}{5}&=&\frac{10}{5} \\&y&=&2 \end{array} The y-intercept is $(0, 2)$. Graph the line by plotting the intercepts and connecting them using a line. (Refer to the graph in the answer part above.) The graph covers all x-values therefore the domain is $(-\infty, +\infty)$. The graph covers all y-values therefore the range is $(-\infty, +\infty)$.
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