1. Do Now. You have 5 minutes.
1. Which of the following is a rational number? a. 3π b. 1.32… c. √44 d Jaselyn rides her bike at a rate of 12 miles per hour. How far does she ride in 10 minutes?

2. Do Now. You have 5 minutes. 1. Which relation is not a function?
B. {(1, -5), (2, -5), (3, -5), (4, -5)}
C. {(-4, -4), (-3, -2), (-2, -1), (-1, 0)}
D. {(6, 4), (7, 5), (8, 6), (8, 7)}
2. Given the relation R = {(-1, 3), (a, 4), (1, 2), (2, 4)}. Which replacement for a makes this relation a function?
a. -1
b. 3
c. 1
d. 2

3. Today’s objective
SWBAT identify and use function notation. We are what we repeatedly do. Excellence, therefore, is not an act but a habit. Aristotle

4. Introduction: What is Function Notation?
f(x) = 2x - 1 y = 2x – 1 f(3) = 2x-1 solve for y = 2x -1 when x = 3
F is a function of x.
F depends on x.
X is my input value.
And f(x) is my output value.
Whatever number is inside my x is the value I would substitute into x.
This is not any different than if I were to right y = 2x -1 and give you a value of x to substitute. Difference is the form in which they’re written.
Show them f(3) for the left side and where x = 3 on the right side.

5. Example 1
Group A wrote the function f(x) = 4x + 2 to represent the breaking weight of a bridge with t layers of paper. f(x) = 4x + 2 What is f(3)? What does it represent?
t = layers of paper
g(t) = breaking weight
What is my input?
What is my output?
The breaking weight is a function of the layer of papers/The breaking weight depends on the layer of papers.
In other words, what does the parenthesis represent? (What you would substitute in.)
What would g(10) represent?

6. Which value is the input? Which value is the output?
Example 2
f(x) = 2(x – 8) and h(t) = 5 + t
Find f(3) ) Find h(10)
Which value is the input?
Which value is the output?

7. Example 3
Example: At a certain market, oranges cost $.90 each. Make a table to show the cost of 1, 2, 3, 4 and 5 oranges.
What is the domain of the table?
What is the range?
What is the independent variable?
What is the dependent variable?
Is this a function?
Write an equation for the cost of any number of oranges using function notation.

8. You Try
1. If f(x) = 3x, find f(4) 2. s(2) if s(t) = 4 + t. Which value is the input? Which value is the output? 3. h(4) if h(t) = 5t + 2

9. Independent practice
Textbook pg. 303: 8-19
Homework: worksheet

10. EXIT Ticket Find the following function values:
1. f(8) if f(x) = 2x + 3
2. f(7) if f(x) = 4x – 5
3. In question 2, which value is the input and which value is the output?

11. EXAMPLE 3
1. Choose 4 values for x to make a function table for f(x) = 3x Now, state the domain and range of the function 3. Identify the independent and dependent variables

12. You Try
1. If f(x) = 3x, find f(4) 2. If s(t) = 4 + t, Find s(2) 3. Choose four values for x to make a function table for f(x) = 4x – 1. Then state the domain and range of the function. Identify the independent and dependent variables.

13. Example 4
Giselle is going to rent a scooter for at least one hour. The fee is $45 plus $5 for each hour it is rented. Write a function rule (in function notation form) to describe the total cost of renting a scooter. Find the number of hours Giselle rented the scooter if the total cost was $65.
Underline function rule. Usually when we see these key words, it means we can just write an equation. However, in this problem, they’re asking us to write it in a specific format. Function notation.
Let’s first figure out what my inputs or outputs are.
What depends on what in this problem?
What is a function of what?
Cost is a function of # of rental hours.
C(h) = h
What we would do to find how many hours Giselle rented the scooter for?
What do we know?
Is total cost the input or the output?
Where should I substitute that?

14. Independent practice Handout For gold round: Textbook: p. 303: 8-19
HOMEWORK: p. 90: 1-6

15. EXIT TICKET
1. Choose four values for x to make a function table for f(x) = x + 5. Then state the domain and range of the function. 2. Find the function value of f(8) if f(x) = 5x BONUS: A dance studio charges an initial fee of $75 plus $8 per lesson. Write a function to represent the cost c(l) for l lessons.