Combinations of Functions

Objective To be able to perform operations and combinations of functions algebraically, graphically, and with the use of technology.

Relevance To be able to model a set of raw data after a function to best represent that data.

Warm Up – Graph the piecewise function.

Operations with Functions: Sum Difference Product Quotient

Example: Let f(x) = 5x² -2x +3 and g(x) = 4x² +7x -5 Find f + g Find f - g

Example:

Using your GDC Start with “VARS”

Example: Let f(x) = 5x² and and g(x) = 3x – 1. Find f · g Find f/g

Example:

Example: f(x)=2x + 3 and g(x) = x -7

Let’s take a look graphically.

Find: 1 + 4 = 5

Find: 0 + - 4 = - 4

Find: 0 - 4 = - 4

Find: 3 - (- 4) = 7

Find: 5 x 4 = 20

Find: - 3 x 5 = - 15

Find: 6 3 = 2

Composition of Functions

A composite function is a combination of two functions. You apply one function to the result of another.

The composition of the function f with the function g is written as f(g(x)), which is read as ‘f of g of x.’ It is also known as which is read as ‘f composed with g of x.” In other words:

Ex: f(x)=2x + 5 and g(x) = x - 3 You can work out a single “rule” for the composite function in terms of x.

Do you think will give you the same result? NO!

You Try…. f(x) = 2x + 2 g(x) = (x + 2)2 Find:

You may need to evaluate a composite function for a particular value of x. Method 1: Work out the composite function. Then substitute 3 for x.

You may need to evaluate a composite function for a particular value of x. Method 2: Substitute 3 into g(x). Substitute that value into f(x).

Now, let’s take a look at it graphically……

Find:

Find:

Find:

Find:

Find: