Intermediate Algebra – Student Workbook – Second Edition 2013

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$Lesson 2a – Assessment - Scottsdale Community College - Math Blog$

Lesson 2b – Functions and Function Operations Mini-Lesson Problem 7 MEDIA EXAMPLE – FUNCTION MULTIPLICATION Given ( ) and ( ) , find ( ) ( ) Problem 8 YOU TRY – FUNCTION MULTIPLICATION For each of the following, find ( ) ( ) a) f(x) = 3x – 2 and g(x) = 3x + 2 b) f(x) = 2x 2 + 1 and g(x) = x 3 – 4x + 5 c) f(x) = 4x - 1 and g(x) = (3x) 0 d) f(x) = 4x 3 and g(x) = -6x Scottsdale Community College Page 80 Intermediate Algebra
Lesson 2b – Functions and Function Operations Mini-Lesson Function Division and the Division Property of Exponents When dividing functions, you will also need to work with exponents of different powers. The following should be familiar to you and will come into play in the examples below: DIVISION PROPERTY OF EXPONENTS Let m, n be rational numbers. To divide powers of the same base, keep the base and subtract the exponents. a a m n mn a where a 0 Problem 9 WORKED EXAMPLE – FUNCTION DIVISION For each of the following, find f (x) . Use only positive exponents in your final answer. g(x) a) ( ) and ( ) f ( x) 15x g( x) 3x 5x 5x 159 6 15 9 b) ( ) and ( ) f ( x) 4x 8 g( x) 2x 2x 2x 5 58 3 This is not our final answer, however, as we need to use only positive exponents in our final result. Recall the rule for negative exponents as follows: If a 0 and n is a rational number, then a n 1 n a Let’s use this rule to rewrite as follows: 3 2 f ( x) 2 2x Therefore, our final results are: 3 3 x g( x) x Notice that the -2 on top did not change or impact the exponent in any way. Scottsdale Community College Page 81 Intermediate Algebra
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Scottsdale Community College Interm
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Table of Contents Lesson 1a - Intro
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Lesson 1a - Introduction to Functio
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Lesson 1b - Linear Equations In the
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Lesson 4b - More on Logarithms This
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Lesson 5b - Solving Quadratic Equat
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Lesson 6a - Exponents and Rational
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Lesson 6b - Rational Exponents & Ra
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Lesson 6b - Rational Exponents and
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Appendix A: You Try Answers Lesson
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Appendix A: You Try Answers You Try
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Intermediate Algebra – Student Workbook – Second Edition 2013

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