1. Cornell Notes Section 1.6 Day 2 Section 1.6 Day 3 Section 1.7 Day 1
Summary (3 sentences)
Section 1.6 Day 3
2-3 Questions
Section 1.7 Day 1
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2. Section 1.7 Day 2 Functions
Algebra 1

3. Learning Targets Graph a function by creating a table
Define a function and function notation
Identify a function from a table, ordered pairs, graph, equation, and mapping diagram
Identify a function using the vertical line test
Construct a function in a table, ordered pairs, graph, and mapping diagram
Determine the domain and range of a function from a table, ordered pairs, graph, and mapping diagram
Graph a function by creating a table
Determine function values from an equation
Determine the meaning of function components in a context

4. Graph a function: Equation
To determine if an equation is a function, the easiest method is to graph it.
To do this, we will use a table to create ordered pairs
Example: Is −3𝑥+𝑦=8 a function?
1. Table Graph 3. Passes VLT
Thus, a function! 𝑋 −1 1 2 𝑌 5
4.5 11 14

5. Example 1: Graphing Is 𝒚= −𝒙 𝟐 a function?
1. Table Graph Passes VLT
Thus, a Function X Y −1 1 2 −4

6. Function Notation Functions can be represented by the notation:
𝒇(𝒙)
An equation may look like
𝒚=𝟑𝒙−𝟐
The purpose of this notation is to clearly see the input values and their relationship with the output values. We will take a closer look at this later in the lesson.
In function notation, it becomes
𝒇 𝒙 =𝟑𝒙−𝟐

7. Example 2: Function Values
For 𝑓 𝑥 =−4𝑥+7, find each value
A) 𝑓(2)
𝑓 2 =−4 2 +7
=−8+7=−𝟏
B) 𝑓 −3 +1
𝑓 −3 =−4 −3 +7
=12+7=𝟏𝟗

8. Calculator: Function Values
1. Click “y =”
2. Next to 𝑦 1 = type in the function
3. Click “vars”
4. Click the “right button” to “Y-VARS”
5. Click Function (enter)
6. Click 𝑌 1 (enter)
7. Type (#)
8. Click Enter

9. Example 3: Function Values
For 𝑓 𝑥 =2 𝑡 3 , find each value
A) 𝑓(1)
𝑓 1 =
=2 1 =𝟐
B) 𝑓 3 +3
𝑓 3 +3= =
=54+3=𝟓𝟕

10. Example 4: Function Values
For 𝑓 𝑥 =2𝑥−3, find each value
A) 𝑓(𝑦)
𝑓 𝑦 =𝟐𝒚−𝟑
B) 𝑓(𝑟+6)
𝑓 𝑟+6 =2 𝑟+6 −3
=2𝑟+12−3
=𝟐𝒓+𝟗

11. Interpreting Function Components
Let 𝑓(𝑡) be the number of people, in millions, who own cell phones 𝑡 years after Explain the meaning of the following statements.
A) 𝑓 10 = ,300,000 people own cell phones in 2000
B) 𝑓 𝑎 = ,000,000 people own cell phones a years after 1990
C) 𝑓 20 =𝑏 b million people own cell phones in 2010
D) 𝑛=𝑓(𝑡) n million people own cell phones t years after 1990

12. Example 5: Interpreting
Let 𝑓(𝑡) be the number of people waiting in line for a rollercoaster ride, and 𝑡 be measured in hours after the park opens at 8am. Explain the meaning of the following statements
A) 𝑓 3 = There are 45 people in line at 11am
B) 𝑓 𝑡 = There are 60 people in line 𝑡 hours after 8am
C) 𝑓 5 =𝑎 There are 𝑎 people in line at 1pm
D) Write the following in function notation:
There are 20 people waiting in line for the ride 4pm. 𝑓 8 =20

13. Exit Ticket for Homework
Worksheet