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Adding & Subtracting

Site: Harrison
Course: Michigan Algebra I Sept. 2012
Book: Adding & Subtracting
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Date: Thursday, 21 November 2024, 10:02 PM

Description

Adding and Subtracting

Table of contents

Adding

The four main operations of addition, subtraction, multiplication, and division can also be performed with functions. To add functions, combine like terms.

Example Given f(x) = 2x2 and g(x) = 3x2+ 1, what is f(x) + g(x)?

Step 1. Replace f(x) and g(x) with their equivalent expressions.

f(x) + g(x)

(2x2) + (3x2 + 1)

Step 2. Eliminate the parentheses and combine like terms.

2x2 + 3x2 + 1

5x2 + 1

Subtracting

To subtract functions, first change the sign of every term being subtracted using the Distributive Property. Eliminate the parentheses and combine like terms.

Example Given f(x) = 2x2 and g(x) = 3x2+ 1, what is f(x) - g(x)?

Step 1. Replace f(x) and g(x) with their equivalent expressions.

f(x) - g(x)

(2x2) - (3x2 + 1)

Step 2. Use the Distributive Property to change the sign of every term of g(x).

2x2 - 3x2 - 1

Step 3. Combine like terms.

-1x2 - 1 or -x2 - 1


Evaluating

Functions can also be added or subtracted given a domain value. First evaluate each function for the given domain then perform the indicated operation using the output values.

Example If f(x) = 2x2 and g(x) = 3x2 + 1, what is f(2) + g(3) ?

Step 1. Evaluate each function

f(2) = 2(2)2 = 8

g(3) = 3(3)2 + 1 = 28

Step 2. Add the output values of the two functions

f (2) + g(3)

= 8 + 28

= 36

Video Lesson

To learn how to add and subtract functions, please select the following link:

Add and Subtract Functions

Practice

Add and Subtract Functions Worksheet

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Answer Key

Add and Subtract Functions Answer Key

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Sources

Embracing Mathematics, Assessment & Technology in High Schools; A Michigan Mathematics & Science Partnership Grant Project

Holt, Rinehart & Winston, "Adding and Subtracting Functions." http://my.hrw.com/math06_07/nsmedia/lesson_videos/alg2/player.html?contentSrc=6480/6480.xml (accessed 8/10/2010).

Kuta Software, www.kutasoftware.com/free.html (accessed 07/19/2010).

Stapel, Elizabeth. "Function Notation: Introduction/Evaluation." http://www.purplemath.com/modules/fcnnot.htm (accessed 7/15/2010).