1. Brought to you by Tutorial Services – The Math Center
FUNCTIONS
Brought to you by
Tutorial Services – The Math Center

2. Functions WHAT IS A FUNCTION? DOMAIN AND RANGE EVEN AND ODD FUNCTIONS
ONE-TO-ONE FUNCTIONS

3. 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 x
dependent y
For Example: -1, 0 , 1
If x = 1, then y = 0
Or if x = 2, then y = 4

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

5. WHAT IS A FUNCTION? Example: (continued) y = mx + b y = x + 2
x = any real #
Choosing x = -1,0,1 Yields,
y = 1x + 2 ;
y = 1*(-1) + 2 = 1
y = 1*(0) + 2 = 2
y = 1*(1) + 2 = 3

6. DOMAIN AND RANGE DOMAIN RANGE Any possible value of x is the domain.
Any possible value of y is the range.
Examples:
Examples:
{ y| y < 0 }
{ x| x > 4 }
{ y| y > 5 }
{x| x is all real numbers }

7. 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).
Example:
y = x2
Example:
y = x3

8. EVEN & ODD FUNCTIONS EVEN FUNCTIONS ODD FUNCTIONS Ex. y = x2

9. 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

10. Tutorial Services – The Math Center
Brought to you by
Tutorial Services – The Math Center
QUESTIONS?

11. Functions Links Functions Workshop Handout
Analysis of Functions Handout
Algebraic and Logarithmic Functions Handout
Functions Quiz