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Warm Up

Warm Up. Find your place!. Lesson 12. Functions. Functions. Defn : A function is a relation where there is only one y -value for each x -value NB :. Functions. Mapping Diagram Ex. Which of the following is a function?. Function. Not a function. x. y. x. y. Functions.

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Warm Up

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  1. Warm Up Find your place!

  2. Lesson 12 Functions

  3. Functions Defn: A function is a relation where there is only one y-value for each x-value NB:

  4. Functions Mapping Diagram Ex. Which of the following is a function? Function Not a function x y x y

  5. Functions Cartesian graph Ex. Which of the following is a function?

  6. Functions Vertical Line Test: To verify whether a graph represents a function you must be able to draw a vertical line anywhere and intersect the function at one point only. If it is possible to intersect at two points it is not a function. Ex.

  7. Functions Cartesian graph Ex. Which of the following is a function? Function Not a function

  8. Functions Set of ordered pairs Ex. Which of the following is a function? {(0,1), (1,1), (2,8), (3, 27)} Function {(0,0), (1,-1), (1,1), (4, 2)} Not a function

  9. Properties of Functions Domain: All possible x-valuesof the function Range: All possible y-valuesof the function Ex. Find the Domain and Range of the function: domf :{-1, 0, 1} ran f : { 0, 1}

  10. Properties of Functions Ex. Find the Domain and Range of the function: domf :{-2, 3} ran f : { -2, 2} domf :{-2, 2} ran f : {1,4}

  11. Properties of Functions Ex. Find the Domain and Range of the function: domf :{-∞, + ∞} ran f : { -2, + ∞} domf :{-2, + ∞} ran f : {-∞,2}

  12. Properties of Functions Zero: Value of x(s) when y=0 (x, 0) (ie. x-intercept) Initial Value: Value of y (s) when x=0 (0, y) (ie. y-intercept)

  13. Properties of Functions Ex. Find the zero(s) and the initial value of the following function: Zero(s): -1 & 1 Init Val: 2

  14. Properties of Functions Ex. Find the zero(s) and the initial value of the following function: Zero(s): 2 Init Val: 1

  15. Properties of Functions Ex. Find the zero(s) and the initial value of the following function: Graphically Zero(s): 0 & 2 Init Val: 0

  16. Properties of Functions Ex. Find the zero(s) and the initial value of the following function: Algebraically - Zero(s)

  17. Properties of Functions Ex. Find the zero(s) and the initial value of the following function: Algebraically - Init Val.

  18. Homework Workbook P. 48 #2 P. 50 #7 P. 52 #9, 11 & 12 P. 54 #14 & 15

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