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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 x dependent y 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 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

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 }

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

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

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

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