1. Warm-up 1.7 Evaluate the equation y = 2x + 7 for: X = -2 X = 5 X = ½
1.7 Function Notation

2. HW Review
1.7 Function Notation

3. 1.7 Function Notation Objective: TSWBAT
write functions using function notation
Determine an appropriate linear model for a real-life situation

4. Function Notation
Some sets of ordered pairs can be described by using an equation.
We can represent these using function notation.

5. Function Notation ƒ(x) = 5x + 3 ƒ(1) = 5(1) + 3
Output value
Input value
Output value
Input value
ƒ(x) = 5x + 3
ƒ(1) = 5(1) + 3
ƒ of x equals 5 times x plus 3.
ƒ of 1 equals 5 times 1 plus 3.

6. Function Notation
The function described by ƒ(x) = 5x + 3 is the same as the function described by y = 5x + 3.
y = 5x is the same as
ƒ(x) = 5x + 3

7. Function Notation
The graph of a function is a picture of the function’s ordered pairs on a coordinate plane.

8. Caution
f(x) is not “f times x” or “f multiplied by x.” f(x) means “the value of f at x.” So f(1) represents the value of f at x =1
Caution

9. Example 1 For each function, evaluate ƒ(0), ƒ , and ƒ(–2).
ƒ(x) = 8 + 4x
Substitute each value for x and evaluate.
ƒ(0) = 8 + 4(0) = 8
ƒ = = 10
ƒ(–2) = 8 + 4(–2) = 0

10. Dependent and Independent Variables
The output f(x), is the dependent variable because it depends on the input value of the function.
The input x, is called the independent variable.

11. Graphing a Function
Independent variable x, is graphed on the horizontal axis
Dependent variable f(x), is graphed on the vertical axis.

12. Linear Models
Most cell phone rate plans are a linear function of some kind.
Example plan: you pay $20 a month for your cell phone and 5 cents per minute of usage
The monthly cost of using your cell phone would be a linear equation or a function, C, based on the number of minutes you use monthly and the monthly phone cost.

13. Linear Models
Can you come up with a linear model (function) in slope-intercept form that correctly models the rate plan described?
What variables do you choose? Why?
Which variable is the dependent variable? Why? Independent variable? Why?

14. Check 1. f(x) = 9 – 6x 9; 6; 21 2. 4; 6; 0 3. Graph f(x)= 4x + 2.
For each function, evaluate
1. f(x) = 9 – 6x
9; 6; 21 2.
4; 6; 0
3. Graph f(x)= 4x + 2.
1.7 Function Notation

15. Making a Linear Model from a real-life situation
Identify the Independent (x) and dependent (y) variable
Make a function
Make a table of values!
Graph to show visually!
1.7 Function Notation

16. Example 1 You make $25 an hour babysitting
Write a function that represents this situation
Graph it!
1.7 Function Notation

17. Example 2
You receive $50 from your grandmother. Afterwards, She will give you $5 a week for allowance
Write a function representing this scenario
What is the independent variable represent? The dependent?
1.7 Function Notation

18. Example 3
In 2013, Kapernick was paid around $50,000 per game. Write a function showing this scenario.
1.7 Function Notation

19. Example 4
You are selling tickets to the school dance. Each ticket costs $10. You have $20 left over from last year’s ticket sales. Write a function that represents this scenario.
1.7 Function Notation

20. Example 5
Today you are 40 inches tall, if you grow at a rate of 2 inches per year, write a function demonstrating this scenario.
Graph it!
1.7 Function Notation

21. Example 6
You are really hungry. You just had a really long workout. You go to In and Out and you really want burgers, animal style. There are 330 calories per burger. Make a linear model representing this scenario. Graph it.
1.7 Function Notation

22. Example 7
You weigh 175 pounds. With each animal burger you eat, you will gain 1 more pound. Write a function representing this situation.
1.7 Function Notation

23. Example 8
Ms. Stine is having a quiz on Friday. You get 5 points for every correct question. Write a linear model representing this situation
If there are 21 questions, what is the maximum score you can get
1.7 Function Notation

24. Example 9
It is midday and it is 90 degrees outside. Every hour, the temperature drops 5 degrees. Write a linear model representing this situation. What domain makes sense? Range?
1.7 Function Notation

25. Example 10
Devin is unhappy that he does not have a girlfriend. He decides to go on 2 OKCupid dates a week. Make a linear model for this situation. What is a reasonable domain? Range?
1.7 Function Notation

26. Reflection
Let’s say we are going on a trip. We are driving and we average 60 miles per hour.
What function would correctly model the distance (D) we travel in a certain number of hours (t)?

27. Homework Page 55 Page 56 Page 95 21, 22, 33, 34, 36 45-48
48 a, b, and c
1.7 Function Notation

28. Homework
1.7 Function Notation