FUNCTIONS
Brought to you by
Tutorial Services – The Math Center
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?
Brought to you by
Tutorial Services – The Math Center
Functions Links
• Functions Workshop Handout
• Analysis of Functions Handout
• Algebraic and Logarithmic Functions Handout
• Functions Quiz