#### Transcript of 9.1 Exploring Combinations of Functions

**9.1 Exploring Combinations of Functions**

Example #1

More Examples

Question 1: What operation must be used to combine the following functions in order to get a y-intercept of 22?

Answers

Predict which equations match with which graphs.

Sinusoidal

Periodic

Characteristics

Sinusoidal

Decreases exponentially

Range {y>=0}

V.A. at x=0

There are several different ways to combine functions including:

addition (f+g)(x)

subtraction (f-g)(x)

multiplication (f*g)(x)

division (f/g)(x)

composition (f g)(x)

Introduction

It is possible to combine two or more simple functions into one complex function.

The characteristics of the individual functions that are combined will effect the properties and characteristics of the function that is created.

Typical questions involve:

determining the parent functions from the graph of combined functions

determining the operation that must be used to combine two functions and obtain another given function.

Question 3: How would you combine the following functions in order to get a function of the order 5?

f(x)=10x+17 g(x)=-3x-5

f(x)= x^3+2 g(x)=x^2+3x+2

Question 2: What operation could be used to combine the followng equations in order to get a hole at x=-5?

f(x)=x^2+3x-10 g(x)=x^2+4x-5

**Liana, Rana, Sabrina & Rhea**

NOW FOR THE ACTIVITY...

Get into groups of 3 or 4!

How must the following equations be combined in order to produce a function where x cannot equal -2?

f(x)=x+2 g(x)=2x^2-x-6

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