1. Use function notation to evaluate and interpret functions
Lesson 3.3
Essential Question: How can you use function notation to represent a function?
Objectives:
Use function notation to evaluate and interpret functions
Use function notation to solve and graph functions
Solve real-life problems using function notation.
Review:
Function – is a rule or math problem that shows a relationship between
two quantities.
Input / domain / x-value – is the independent variable.
Output / range / y-value – is a dependent variable
Function notation
In general, the symbol f(x) replaces y and is read as “the value of f at x” or “f of x”. It does not mean f times x. f(x) is called function notation.
Fun Fact: f(x) notation first used in early 1700’s by a guy named Leonard Euler

2. Table showing the results of a function
Objective 1: Use function notation to evaluate and interpret functions
Interpreting function notation:
a. Y = 2x – 3 we read as Y is the dependent difference between the value of two times “x” and 3
b. f(x) = 2x-3 we read as the function of x is the difference between the value of two time “x” and 3
Input
(x)
Output (y) 1 5 2 8
(x)
f(x) 1 5 2 8
Table showing the results of a function
A function table

3. Evaluating a function:
Objective 1: Use function notation to evaluate and interpret functions
Evaluating a function:
f(x)= -4x+7 when x=2 and x= -2
f(x)= -4x + 7
Write the function
f(x)= -4x + 7
f(2)= -4(2) + 7
Substitute for x
f(-2)= -4(-2) + 7
= -8+ 7
Multiply
= 8 + 7
= -1
Add
= 15
When x=2, f(x)= -1 and when x= -2, f(x)=15

4. Rewrite the function as
Objective 2: Use function notation to solve and graph functions
Graph x y
When x= 0 and x= 2
Rewrite the function as
Plot (0, 3) & (2,2).
Draw a line connecting the 2 points
Note: The red triangle that was created what is it related too?

5. Objective 3: Solve real-life problems using function notation
Graph the function
A helicopter has a range of 350 miles. Traveling at 125 miles an hour how far will the helicopter travel after 1, 2, and 3 hours. Create a function that represents distanced traveled. x y
Write the function
400
f(x)= x
Create the table
300
(x)
f(x)
350 1
225 2
100 3
-25
200
100
crash 1 2 3

6. Write a summary of how function notation is used
Have we answered the essential question?
SUMMARY CLIP
Write a summary of how function notation is used