Homework Answers

QUIZ TIME After you finish work on the warm up Why did the skeleton visit a butcher shop?

Function Notation Materials: handout (Why did the skeleton visit a butcher shop?), graph paper, quizzes

In this lesson you will Learn to use function notation Use a graph to evaluate a function for various input values Use an equation to evaluate a function for various input values

Definitions Relation A relationship between sets of information. Typically between inputs and outputs. Function A relation such that there is no more than one output for each input

4 Examples of Functions X Y 10 2 15 -5 18 20 1 7 X Y -3 1 -1 4 5 7 3

3 Examples of Non-Functions Y 4 1 10 2 11 -3 5 3

Which do you prefer to write? Function Notation The f is the name of the function machine and the value inside the parentheses is the input. The expression to the right of the equal sign shows what the machine does to the input. Which do you prefer to write? Evaluate f when x = 25? f(25) OR 5

Example If f(x) = 2x + 3, find f(5). When evaluating, do not write f(x)! You want x=5 since f(x) was changed to f(5) You wanted to find f(5). So the complete final answer includes f(5) not f(x)

Substitute and Evaluate Solving v. Evaluating No equal sign Equal sign Substitute and Evaluate The input (or x) is 3. Solve for x The output is -5.

EXAMPLE You can use the function f(x)=19.4+1.28x to approximate the wind chill temperature for a given actual temperature when the wind speed is 15 miles per hour. Both x and are in degrees Fahrenheit. Find f (x) for each given value of x. a. f(-10) b. f(0) c. x when f(x)=19 d. x when f(x)=-13 a) 6.6 b) 19.4 c) -.3125 d) -25.3125

Not all functions are expressed as equations. Here is a graph of a function g. The equation is not given, but you can still use function notation to express the outputs for various inputs. For example, g(0)=3, g(4)=6, and g(6)=1. Can you find x-values for which g(x)=3?

Look at the graph below. What is the domain. What is the range Look at the graph below. What is the domain? What is the range? Use the graph to find each function value in the table. Then do the indicated operations. Domain: [0, 25] Range: [0, 20]

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Homework: Packet p. 3 Tutorials: Mondays and Thursdays Homework: Packet p. 3 Tutorials: Mondays and Thursdays. 1st half of lunch