FUNCTIONS

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Functions

• WHAT IS A FUNCTION?

• DOMAIN AND RANGE

• EVEN AND ODD FUNCTIONS

• ONE-TO-ONE FUNCTIONS

WHAT IS A FUNCTION?• A function can be described as having an

independent variable and a dependent variable.

• Also, the value of the independent variable cannot

be repeated. • The independent variable can be any number

• The dependent variable changes as the independent variable changes

Independent ydependentx

For Example: -1, 0 , 1

If x = 1, then y = 0 Or if x = 2, then y = 4

WHAT IS A FUNCTION?Example: Linear Equations

y = mx + b

• m = slope• b = y-intercept (Where x = 0)• y = Dependent Variable• x = Independent Variable

WHAT IS A FUNCTION?Example: (continued)

y = mx + b

Choosing x = -1,0,1

Yields,

y = 1*(-1) + 2 = 1y = 1*(0) + 2 = 2y = 1*(1) + 2 = 3

m = 1b = 2

x = any real #

y = x + 2

y = 1x + 2 ;

DOMAIN AND RANGE

DOMAIN• Any possible value

of x is the domain.

RANGE• Any possible value

of y is the range.Examples: Examples:

{ x| x > 4 }

{x| x is all real numbers }

{ y| y < 0 }

{ y| y > 5 }

EVEN AND ODD FUNCTIONS

• A Function is of even degree if both ends go either up or down. (The highest exponent is even)

• A function is of odd degree if it rises to the right and falls to the left or vice versa. (The highest exponent is odd).

y = x2

y = x3

Example:

Example:

EVEN & ODD FUNCTIONSEVEN FUNCTIONS ODD FUNCTIONS

Ex. y = x2 Ex. y = x3

ONE-TO-ONE FUNCTIONS

• Functions that assign unique outputs from unique inputs.

• x1 and x2 are real numbers.

• If f(x1) f(x2) and where x1 x2, then the function is one-to-one.

• This test is sometimes called the Horizontal Line Test.Examples:

y = x + 3 y = x3 + 9

QUESTIONS?

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Functions Links

• Functions Workshop Handout

• Analysis of Functions Handout

• Algebraic and Logarithmic Functions Handout

• Functions Quiz