## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson

# Chapter 7 - Functions and Graphs - 7.2 Domain and Range - 7.2 Exercise Set - Page 459: 49

#### Answer

Domain: $\{p\in \mathbb{R}\ |\ 0\lt p\leq 10.60\}$ or $(0,10.60]$ (if we expect price to be possibly 0, then $\{p\in \mathbb{R}\ |\ 0\leq p\leq 10.60\}$ or $[0,10.60]$)

#### Work Step by Step

If a function is used as a model for an application, the problem situation may require restrictions on the domain. For example, length and time are generally nonnegative, and a person's age does not increase indefinitely. $A(p)=-2.5p+26.5 \quad$ can be calculated for any real number t, but we expect price to be a positive amount, $p\gt 0.$ Also, we expect the amount $A(p)$ to be nonnegative, $-2.5p+26.5 \geq 0$ $26.5\geq 2.5p$ $\displaystyle \frac{26.5}{2.5}\geq p$ $10.6\geq p$ Domain: $\{p\in \mathbb{R}\ |\ 0\lt p\leq 10.60\}$ or $(0,10.60]$ (if we expect price to be possibly 0, then $\{p\in \mathbb{R}\ |\ 0\leq p\leq 10.60\}$ or $[0,10.60]$)

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