## Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole

# Chapter 2 - Section 2.1 - Functions - Exercises: 27

#### Answer

Evaluate $k(x) = -x^2 - 2x +3$: $k(0) = 3$ $k(2) = -5$ $k(-2) = 3$ $k(\sqrt 2) = 1 - 2\sqrt2 = -1.828$ $k(a+2) = -a^2-6a-3$ $k(-x) = -x^2+2x+3$ $k(x^2) = -x^4-2x^2+3$

#### Work Step by Step

For x = 0 $k(0) = -(0)^2 - 2(0) +3$... square 0 $=-(0) - 2(0) +3$...multiply 0 by -1 $=0-2(0)+3$...multiply 0 by 2 $=0-0+3 = 3$ ____________________ For x = 2 $k(2) = -(2)^2 - 2(2) +3$... square 2 $=-(4) - 2(2) +3$...multiply 4 by -1 $=-4-2(2)+3$...multiply 2 by 2 $=-4-4+3 = -5$ ____________________ For x = -2 $k(-2) = -(-2)^2 - 2(-2) +3$... square -2 $=-(4) - 2(-2) +3$...multiply 4 by -1 $=-4-2(-2)+3$...multiply -2 by 2 $=-4-(-4)+3 = 3$ ____________________ For x = $\sqrt 2$ $k(\sqrt 2) = -(\sqrt 2)^2 - 2(\sqrt 2) +3$... square $\sqrt 2$ $=-(2) - 2(\sqrt 2) +3$...multiply 2 by -1 $=-2-2\sqrt 2+3$...simplify $=1 - 2\sqrt2 = -1.828$ ____________________ For x = a + 2 $k(a+2) = -(a+2)^2 - 2(a+2) +3$... square $a + 2$ $=-(a^2+4a+4) - 2(a+2) +3$...multiply quadratic by -1 $=-a^2-4a-4-2(a+2)+3$...multiply $a+2$ by -2 $=-a^2-4a-4-2a-2+3$...simplify $=-a^2-6a-3$ ____________________ For x = -x $k(-x) = -(-x)^2 - 2(-x) +3$... square -x $=-(x^2) - 2(-x) +3$...multiply $x^2$ by -1 $=-x^2-2(-x)+3$...multiply -x by -2 $=-x^2+2x+3$ ____________________ For x = $x^2$ $k(x^2) = -(x^2)^2 - 2(x^2) +3$... square $x^2$ $=-(x^4) - 2(x^2) +3$...multiply $x^4$ by -1 $=-x^4-2(x^2)+3$...multiply $x^2$ by -2 $=-x^4-2x^2+3$ ____________________

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