1. Evaluating Functions

2. 2. For the graph, evaluate ƒ(0), ƒ(.5) , and ƒ(–2).
1. For ƒ(x) = 5x + 3
Evaluate ƒ(0)=
ƒ(-1)= and ƒ(–2) =
2. For the graph, evaluate ƒ(0),
ƒ(.5) , and ƒ(–2).
3. Evaluate ƒ(0), ƒ , and ƒ(–2)
for ƒ(x) = x2 – 4x
4. Graph the function f(x) = 2x + 1.
5. A painter charges $200 plus $25 for each can of paint used.
a. Write a function to represent the total charge for a certain number of cans of paint.
b. Evaluate f(4), and state what it represents?

3. The function described by ƒ(x) = 5x + 3 is the same as the function described by y = 5x + 3. And both of these functions are the same as the set of ordered pairs (x, 5x+ 3).
y = 5x (x, y) (x, 5x + 3)
Notice that y = ƒ(x) for each x.
ƒ(x) = 5x (x, ƒ(x)) (x, 5x + 3)

4. Example 1: Evaluating Functions
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

5. f(1)= 8 for f(x) = 5x + 3 (1, 8) for y = 5x + 3 ƒ(x) = 5x + 3
Notes #1: Notation and Evaluating Functions
ƒ(x) = 5x + 3
ƒ of x equals 5 times x plus 3.
f(1)= 8 for f(x) = 5x + 3
(1, 8) for y = 5x + 3
For the function, evaluate ƒ(0)= ƒ(-1)= and ƒ(–2) =

6. Notes #2: Evaluating Functions
For each function, evaluate ƒ(0), ƒ , and ƒ(–2).
Use the graph to find the corresponding y-value for each x-value.
ƒ(0) = 3
ƒ = 0
ƒ(–2) = 4

7. Notes #3: Evaluating Functions
For each function, evaluate ƒ(0), ƒ , and ƒ(–2).
ƒ(x) = x2 – 4x

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

9. Example 3A: Function Application
A local photo shop will develop and print the photos from a disposable camera for $0.27 per print.
Write a function to represent the cost of photo processing.
Let x be the number of photos and let f be the total cost of the photo processing in dollars.
Identify the variables.
Cost depends on the number of photos processed
Cost = 0.27  number of photos processed
f(x) = 0.27x
Replace the words with expressions.

10. Notes 3B: Function Application
A local photo shop will develop and print the photos from a disposable camera for $0.27 per print.
What is the value of the function for an input of 24, and what does it represent?
f(24) = 0.27(24)
Substitute 24 of x and simplify.
= 6.48
The value of the function for an input of 24 is 6.48.
This means that it costs $6.48 to develop 24 photos.

11. Notes #5: Function Application
A painter charges $200 plus $25 for each can of paint used.
a. Write a function to represent the total charge for a certain number of cans of paint.
t(c) = c
b. What is the value of the function for an input of 4, and what does it represent?
300; total charge in dollars if 4 cans of paint are used.