7.3 Power Functions and Function

OperationsBy: Jon Boscan

Sean BoylesEthan Cieply

SWBAT perform operations with functions including power functions

Power Functions and Function Operations

To solve real life problems, such as finding the height of a dinosaur!

Why do I need this?

Power Function- is a common type of function which has the form y=ax^b is a linear function when b=1 a quadratic function when b=2 and the cubic function when b=3.

Vocabulary

ADDITION SUBTRACTION MULTIPLICATION DIVISION

The Operations of Functions

Let F and G be any two functions. A new function h, can be defined by performing any of the four basic operations. (addition, Subtractions, Multiplication, and Division.)

Example f(x)=2x, g(x) = x+1

Operations of Functions (cont.)

Operation of Addition The example is F(x)=2x,g(x)=x+1 Definition H(x)=f(x)+g(x) Equal H(x)=2x+(x+1)=3x+1

Operations of Addition

Operation for subtraction h(x)=f(x)-g(x) Definition is H(x)=f(x)-g(x) Example is f(x)=2x,g(x)=x+1 Would equal h(x)=2x-(x+1)=x-1

Operation of Subtraction

Example is f(x)=2x,g(x)=x+1 Multiplication =h(x)=f(x) times g(x) H(x)= (2x)(x+1)=

Operation of Multiplication

xx 22 2

Operation Of Division H(x)=

H(x)=

)(

)(

xg

xf

)1(

2

xx

F(x)=

g(x)=

F(x)+g(x) =

=

Addition Example

11

)6(2 xx

2/144 xx

2/144 xx

xx 66 2/1

Subtraction Example

2/188 xx x2 )6( x 2/188 xx

F(x) times g(x)=

Multiplication example

xx 62 x12

Division Example

)(

)(

xg

xf

3

1

6

2

x

x