1. 2.1.4: Function Notation and Evaluating Functions
Do Now
If 9(x − 9) = −11, then x = ?
2.1.4: Function Notation and Evaluating Functions

2. GOOD THINGS!!
2.1.3: Domain and Range

3. 2.1.4: Function Notation and Evaluating Functions

4. 2.1.4: Function Notation and Evaluating Functions
Policy Review
Cell phones
Sleeping
Materials
2.1.4: Function Notation and Evaluating Functions

5. 2.1.4: Function Notation and Evaluating Functions
Warm Up
Page 25
A farmer wants to convert 3 greenhouses to solar power.
The smallest greenhouse needs 1,500 square feet of solar panels; the middle and largest greenhouses need 2,100 and 2,800 square feet of panels, respectively.
The farmer gets bids from 3 different companies, each with different pricing.
2.1.4: Function Notation and Evaluating Functions

6. 2.1.4: Function Notation and Evaluating Functions
Warm Up
Company A charges $2,000 for installation per building and $2.00 per square foot of panels. The function for this situation is f(x)= (x).
Company B charges $3,000 for installation per building and $1.50 per square foot of panels. The function for this situation is f(x)= (x).
Company C charges $4,200 for installation per building and $1.00 per square foot of panels. The function for this situation is f(x)= x.
2.1.4: Function Notation and Evaluating Functions

7. 2.1.4: Function Notation and Evaluating Functions
Warm Up: Info Review
Greenhouses
Small
Medium
Large
1500 sq. ft.
2100 sq. ft.
2800 sq. ft.
Pricing Functions
Company A
Company B
Company C
f(x)= (x)
f(x)= (x)
f(x)= x
8 minutes independent
8 minutes partner
2.1.4: Function Notation and Evaluating Functions

8. Company A: f(x) = 2000 + 2(1500) = 2000 + 3000 = 5000
Which company will charge the least for the smallest greenhouse?
The smallest greenhouse requires 1,500 square feet of solar panels, so evaluate A, B, and C at 1,500.
Company A: f(x) = (1500) = = 5000
Company B: f(x) = (1500) = =5250
Company C: f(x) = (1500) = 5700
Company A’s bid is the lowest, at $5,000, so it has the least expensive plan for the smallest greenhouse.
2.1.4: Function Notation and Evaluating Functions

9. Company A: f(x)= 2000 + 2(2100) = 2000 + 4200=6200
Which company will charge the least for the middle greenhouse?
The middle greenhouse requires 2,100 square feet of solar panels, so evaluate A, B, and C at 2,100:
Company A: f(x)= (2100) = =6200
Company B: f(x)= (2100) = =6150
Company C: f(x)= (2100) = 6300
Company B’s bid is the lowest, at $6,150, so it has the least expensive plan for the middle greenhouse.
2.1.4: Function Notation and Evaluating Functions

10. Company A: f(x) = 2000 + 2(2800) = 2000 + 5600 = 7600
Which company will charge the least for the largest greenhouse?
The largest greenhouse requires 2,800 square feet of solar panels, so evaluate A, B, and C at 2,800:
Company A: f(x) = (2800) = = 7600
Company B: f(x) = (2800) = = 7200
Company C: f(x) = (2800) = 7000
Company C’s bid is the lowest, at $7,000, so it has the least expensive plan for the largest greenhouse.
2.1.4: Function Notation and Evaluating Functions

11. If the farmer goes with one company for all three greenhouses, which company will be the least expensive?
Company A = = 18,800
Company B = = 18,600
Company C = = 19,000
Company B’s total bid is lowest, at $18,600, so it has the least expensive plan to complete the project for all three greenhouses.
Connection to the Lesson
Students will be evaluating functions, which requires substitution, as seen in the warm-up.
Students will learn how to evaluate functions like the ones in the warm-up using function notation, which is an easier method to keep track of multiple functions with varying inputs.
2.1.4: Function Notation and Evaluating Functions

12. 2.1.4: Function Notation and Evaluating Functions
BRAIN BREAK!!!!
What is the value of the square?
2.1.4: Function Notation and Evaluating Functions

13. Note Taking
MUST include:
Today’s date (9/6) before you begin notes
Essential Question at top of page
If you see a that’s my hint to you to put that in your notes
Essential Question
How is function notation and evaluating functions related to the coordinate plane?
2.1.3: Domain and Range

14. Introduction Functions f of a variable x are represented by f(x)
The range of f(x) is dependent on its domain
What is range?
What is domain?
2.1.4: Function Notation and Evaluating Functions

15. Introduction, continued
Example: Let f be a function with the domain {1, 2, 3} and let f(x) = 2x
To evaluate this function over the domain {1, 2, 3}, we would substitute each value in the domain for x:
f(1) = 2(1) = 2
f(2) = 2(2) = 4
f(3) = 2(3) = 6
By solving for the function, we find that {2, 4, 6} is the range of f(x).
2.1.4: Function Notation and Evaluating Functions

16. Introduction, continued
Example: Let f be a function with the domain {1, 2, 3} and let f(x) = 3x + 1
f(1) = 3(1) + 1 = 4
f(2) = 3(2) + 1 =7
f(3) = 3(3) + 1 = 10
The range of f(x) is {4, 7, 10}
2.1.4: Function Notation and Evaluating Functions

17. Key Concepts Functions can be evaluated at values and variables
To evaluate a function, substitute the values for the domain for all occurrences of x.
To evaluate f(2) in f(x) = x + 1, replace all x’s with 2
and simplify: f(2) = (2) + 1 = 3. This means that f(2) = 3.
(x, (f(x)) is an ordered pair of a function and a point on the graph of the function.
“x” is the domain, f(x) is the range
2.1.4: Function Notation and Evaluating Functions

18. Common Errors/Misconceptions
Function Notation is NOT a multiplication equation
f(x) does NOT mean “f times x”
2.1.4: Function Notation and Evaluating Functions

19. Work with your elbow partner. Write down answers to check as a class.
Partner Practice
Work with your elbow partner.
Write down answers to check as a class.
Evaluate f(x) = 4x – 7 over the domain {1, 2, 3, 4}. What is the range?
2.1.4: Function Notation and Evaluating Functions

20. To evaluate f(x) = 4x – 7 over the domain
Guided Practice
To evaluate f(x) = 4x – 7 over the domain
{1, 2, 3, 4}, substitute the values from the domain into f(x) = 4x – 7.
2.1.4: Function Notation and Evaluating Functions

21. Guided Practice Evaluate f(1).
f(x) = 4x – 7
Original function
f(1) = 4(1) – 7
Substitute 1 for x.
f(1) = 4 – 7 = –3
Simplify.
2.1.4: Function Notation and Evaluating Functions

22. Guided Practice Evaluate f(2).
f(x) = 4x – 7
Original function
f(2) = 4(2) – 7
Substitute 2 for x.
f(2) = 8 – 7 = 1
Simplify.
2.1.4: Function Notation and Evaluating Functions

23. Guided Practice Evaluate f(3).
f(x) = 4x – 7
Original function
f(3) = 4(3) – 7
Substitute 3 for x.
f(3) = 12 – 7 = 5
Simplify.
2.1.4: Function Notation and Evaluating Functions

24. Guided Practice Evaluate f(4).
f(x) = 4x – 7
Original function
f(4) = 4(4) – 7
Substitute 4 for x.
f(4) = 16 – 7 = 9
Simplify.
2.1.4: Function Notation and Evaluating Functions

25. ✔ Guided Practice Collect the set of outputs from the inputs.
What is the range?
The range is {–3, 1, 5, 9} ✔
2.1.4: Function Notation and Evaluating Functions

26. Independent Practice
Evaluate g(x) = 3x + 1 over the domain {0, 1, 2, 3}. What is the range? Graph the function.
2.1.4: Function Notation and Evaluating Functions

27. Independent Practice, pt. 2 g(x) = 3x + 1 Range: {2, 4, 10, 28} Graph:
Is the point (0, 5) on this graph???
2.1.4: Function Notation and Evaluating Functions

28. Guided Practice
Raven started a petition calling for more vegetarian options in the school cafeteria.
So far, the number of signatures has doubled every day.
She started with 32 signatures on the first day.
Raven’s petition can be modeled by the function f(x) = 32(2)x
Evaluate f(3) and interpret the results in terms of the petition.
2.1.4: Function Notation and Evaluating Functions

29. f(x) = 32(2)x f(3) = 32(2)3 f(3) = 32(8) f(3) = 256
Guided Practice: Raven’s petition
Evaluate the function.
f(x) = 32(2)x
f(3) = 32(2)3
f(3) = 32(8)
f(3) = 256
2.1.4: Function Notation and Evaluating Functions

30. X y range domain input output Guided Practice: Raven’s petition
Interpret the results.
On day 3, the petition has 256 signatures.
This is a point (3, 256) on the graph of the function f(x)=32(2)x
**3 is the INPUT, 256 is the OUTPUT X y
range
domain
input
output
2.1.4: Function Notation and Evaluating Functions

31. Guided Practice: Raven’s petition
Number of signatures
Days ✔
Input = x
Output = y
2.1.4: Function Notation and Evaluating Functions

32. 2.1.4: Function Notation and Evaluating Functions
PARTY TIME (pg. 29)
A company is throwing a large party requiring a venue, tables, chairs, and waiters. There will be between 50 and 200 guests, so the party coordinator has been asked to predict the total cost of the event for 50, 100, 150, and 200 guests. The functions below describe the number of tables, chairs, and waiters needed, as well as the size of the venue in square feet. In each equation, x represents the number of guests.
2.1.4: Function Notation and Evaluating Functions

33. 2.1.4: Function Notation and Evaluating Functions
PARTY TIME pt. 2
Tables are $50 each, chairs are $3 each, waiters earn $100 each, and venues charge $2 per square foot.
Total cost estimate:
2.1.4: Function Notation and Evaluating Functions

34. 2.1.4: Function Notation and Evaluating Functions
PARTY TIME Questions
a. What is the domain of t(x)? b. What is the domain of c(x)? c. What is the domain of w(x)? d. What is the domain of s(x)? e. What is the domain of P(x)? f. What is the most the venue can cost? g. What is the cost for tables and chairs for 100 guests? h. What is the entire cost of the party for 150 guests? i. What is the least amount the party can cost? j. Complete a table of values for the costs of the party.
2.1.4: Function Notation and Evaluating Functions

35. 2.1.4: Function Notation and Evaluating Functions
PARTY TIME Table
# Guests
Tables t(x)
Chairs c(x)
Waiters w(x)
Venue v(x)
Total Cost 50
100
150
200
2.1.4: Function Notation and Evaluating Functions

36. 2.1.4: Function Notation and Evaluating Functions
Exit Ticket
Pull out 1 sheet of paper
Due by end of class
1. Evaluate f(x) = 2x +4 over the domain {0, 1, 2, 3}. What is the range of f(x)?
2. Is the point (1,7) a point on the graph of this function? Why or why not?
2.1.4: Function Notation and Evaluating Functions