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# 9.1 Exploring Combinations of Functions

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## Liana Iannucci

on 22 January 2015

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#### 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?
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:
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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