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.

Lesson 3.3

Essential Question: How can you use function notation to represent a function?

Fun Fact: f(x) notation first used in early 1700’s by a guy named Leonard Euler

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

Input

(x)

Output (y)

1 5

2 8

b. f(x) = 2x-3 we read as the function of x is the difference between the value of two time “x” and 3

Table showing the results of a function

A function table

(x) f(x)

1 5

2 8

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

Objective 2: Use function notation to solve and graph functions

Graph

32

1)( xxf

x

y

Rewrite the function as

Plot (0, 3) & (2,2).

Draw a line connecting the 2 points

When x= 0 and x= 2

Note: The red triangle that was created what is it related too?

Objective 3: Solve real-life problems using function notation

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

(x) f(x)

0 350

1 225

2 100

3 -25

Write the function

f(x)=350-125x

Create the table

1 2 3

100

300

200

400

crash

Graph the function

Have we answered the essential question?

Write a summary of how function notation is used

SUMMARY CLIP