Algebra Funct assign 33 writing functions, IV DV, notation.notebook

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1 Bellwork Describe the domain and range in each case below. Determine in each case whether the relation is also a function. D: D: R: R: 1

2 9/18 Functions: Building a connection between Independent and Dependent Variables Objective: You will be able to: Evaluate functions. Recognize and use function notation. Identify Independent and Dependent variables in context and apply them to graphs of functions. 2

3 You get a job at Safeway where they pay you $7/hr. The table below represents how much you make on your first day. What could you better label the input and output columns? What does the output depend on? 3

4 Independent Variable are the units for the inputs. On the last slide, the number of hours worked was the independent variable. Dependent Variable are the units for the outputs. On the last slide, the amount of money earned was the dependent variable. We say the dependent variable amount depends on the independent variable amount. 4

5 Identify the Independent and Dependent Variable in each case. In Tucson in the summer, more electricity is used as the temperature goes up and less when the temperature goes down. The cost of mailing a package is based on its weight. The faster you walk, the sooner you get home. 5

6 Examples: In each case, identify the Independent and Dependent Variable in each case. The more water you use, the higher your family's water bill. The longer you sit in the theater, the less popcorn you have. When you were little, how tall you were was related to how old you were. 6

7 You get a job at Safeway where they pay you $7/hr. Describe the specific relationship between the number of hours you work and the amount of money you make. 7

8 A Function Rule is an algebraic expression that defines a function. With your Safeway job, your pay, $y, depends on how many hours you work, x. The function rule that defines your pay function would be y=$7x. A function rule is a little input output machine. You input a value for x and the output is f(x) or in the case above, $7x 8

9 With your Safeway job, we said y = $7x, but using function notation we could also write f(x) = $7x 9

10 Writing an equation in function notation for a situation: 1. First, identify the independent and dependent variables. 2. Look for a connection between them. In the problems we start with, the relationship will only involve one math operation: adding, subtracting, multiplying or dividing. 3. Write the rule using function notation. 10

11 Examples of Writing an equation in function notation for a situation: 1. Admission to the movies is $7 per person. How much have to pay for tickets depends on how many people go to the movies. 2. Your parents are trying to lose weight. Each week they lose 1 pound. 3. I can buy 5 doughnuts for $3 and 10 doughnuts for $6. 4. A lawyer charges $200 an hour for her work. 5. One pizza feeds 4 people and 2 pizzas feed 8 people. 11

12 Evaluating Functions Evaluate the given function for each of the given input values. For f(x) = 7x, find f(x) when x = 6 and when x = 10 We understand this in a number of ways: 1. When the input is 6, the output is The point (6, 42) is a point on the function. 3. When you work 6 hours, you earn $42. 12

13 Examples: On your white board, evaluate each function for the given values:

14 Closure At itunes.com you can download a song for $.99. The amount of money you spend depends on how many songs you download. 1. Describe the independent and dependent variables. 2. Write a function rule for this situation. 3. Evaluate your function for 10 and 100 songs downloaded 14

15 Begin HW worksheet 10 minutes on you own and then compare with your partner 15

16 Homework Worksheet 16

17 17

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