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

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

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

5. WHAT IS A FUNCTION? Example: Linear Equations y = mx + b m = slope b = y-intercept (Where x = 0) y = Dependent Variable x = Independent Variable

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

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

8. 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 = x 2 y = x 3 Example:

9. EVEN & ODD FUNCTIONS EVEN FUNCTIONSODD FUNCTIONS Ex. y = x 2 Ex. y = x 3

10. ONE-TO-ONE FUNCTIONS Functions that assign unique outputs from unique inputs. x 1 and x 2 are real numbers. If f(x 1 )  f(x 2 ) and where x 1  x 2, then the function is one-to-one. This test is sometimes called the Horizontal Line Test. Examples: y = x + 3y = x 3 + 9

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

12. Functions Links Functions Workshop Handout Analysis of Functions Handout Algebraic and Logarithmic Functions HandoutAlgebraic and Logarithmic Functions Handout Functions Quiz