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
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