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 Let’s continue our review of functions and function notation, as understanding these topics is CRITICAL for your work in the rest of this course. Functions describe specific relationships between inputs and outputs. Work with the table below as a reminder of how to find inputs and outputs for a given function. If you can learn to think about functions in terms of “inputs” and “outputs”, then the remainder of our topics will be much easier to understand. Problem 2 YOU TRY – FINDING INPUTS, FINDING OUTPUTS Complete the table below. The first one is done for you. Write your results as an ordered pair. Function f(x) = x + 7 (Input, Output) (x, f(x)) Given Input, Find Output Find f(x) when x = 2. Looking for (2, ___) To find the output EVALUATE f(2) ( ) ( ) ( ) ( ) Given Output, Find Input Find x when f(x) = 8. Looking for (___, 8) To find the output, SOLVE for f(x) = 8 ( ) g(t) = 3t – 4 (t, g(t)) Ordered pair: (2, 9) Ordered pair: (1, 8) Find g(t) when t = 4. Find t when g(t) = -1. f(x) = x - 5 Find f(x) when x = -4. Find x when f(x) = 10. g(x) = 2x + 4 Find g(x) when x = 3. Find x when g(x) = 5. Scottsdale Community College Page 76 Intermediate Algebra
Lesson 2b – Functions and Function Operations Mini-Lesson Functions notation can be expanded to include notation for the different ways we can combine functions as described below. Basic Mathematical Operations The basic mathematical operations are: addition, subtraction, multiplication, and division. When working with function notation, these operations will look like this: OPERATION Function Notation – How to Read EXAMPLE Addition f (x)+ g(x) “f of x plus g of x” 3x 2 + 4x Subtraction f ( x) g( x) “f of x minus g of x” (2x + 3) – (4x 2 + 1) Multiplication f ( x) g( x) “f of x times g of x” (3x – 1)(5x + 7) Division f (x) “f of x divided by g of x” 8x 3 2x 1 g(x) 4x Note the g(x) ≠ 0 The examples on the right side of the table may look fairly familiar. That is because you have probably studied these before in a previous class. Many of the problems we will work in this lesson are problems you may already know how to do. You will just need to get used to some new notation. We will start with the operations of addition and subtraction. Problem 3 WORKED EXAMPLE – ADDING AND SUBTRACTING FUNCTIONS Given f(x) = 2x 2 + 3x – 5 and g(x) = -x 2 + 5x + 1. a) find f(x) + g(x) ( ) ( ) ( ) ( ) ( ) ( ) b) find f(x) - g(x) ( ) ( ) ( ) ( ) ( ) ( ) c) find f(1)-g(1) ( ) ( ) [ ( ) ( ) ] [ ( ) ( ) ] ( ) ( ) ( ) ( ) Scottsdale Community College Page 77 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 6a - Exponents and Rational
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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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