1. 1.2(a) Notes: Basics of Functions & Graphs
Date:
1.2(a) Notes: Basics of Functions & Graphs
Lesson Objective: Find the domain and range of functions, and use notation the express the domain and range.
CCSS: F-IF Analyze functions using different representations.
You will need: something to write with ;)
Real-World App: Comparing apples to oranges.

2. Lesson 1: Domain and Range
When you think of the word domain, what first comes to mind?

3. Lesson 1: Domain and Range
When you think of the word domain, what first comes to mind?
1. a field of action, thought, influence, etc.: the domain of science.

4. Lesson 1: Domain and Range
When you think of the word domain, what first comes to mind?
1. a field of action, thought, influence, etc.: the domain of science.
2. the territory governed by a single ruler or government; realm.

5. Lesson 1: Domain and Range
When you think of the word domain, what first comes to mind?
1. a field of action, thought, influence, etc.: the domain of science.
2. the territory governed by a single ruler or government; realm.
3. a region characterized by a specific feature, type of growth or wildlife, etc.: We entered the domain of the pine trees.

6. Lesson 1: Domain and Range
Domain: The set of all first components of a set of ordered pairs in a relation.

7. Lesson 1: Domain and Range
Domain: The set of all first components of a set of ordered pairs in a relation.
Range: The set of all second components of a set of ordered pairs in a relation.

8. Lesson 1: Domain and Range
Find the domain and range of the relation:
{(0, 9.1), (10, 6.7), (20, 10.7), (30, 13.2), (40, 21.2)}
Domain:
Range:

9. Lesson 2: Domain and Range of Graphs
Use the graph to identify the domain and range using notation. A.
Domain:
Range:

10. Lesson 2: Domain and Range of Graphs
Use the graph to identify the domain and range using notation. B.
Domain:
Range:

11. Lesson 3: Functions
What makes a set of items a function?

12. Lesson 3: Functions
What makes a set of items a function?
Function: Each element in the domain corre-sponds to exactly one element in the range.

13. Lesson 3: Functions
Examples:

14. Lesson 3: Functions
Examples:
You can have more than one item valued at the same price, but you cannot have one item valued at two different prices.

15. Lesson 3: Functions Examples:
You can have more than one item valued at the same price, but you cannot have one item valued at two different prices. Graph the following relationships:
Item
Price
Corn 
0.50
 Pear
0.20
 Potato
0.25
 Banana
 0.20
Item
Price
Apple 
0.25
 Orange
0.30
 Tomato
0.35
 0.40

16. Lesson 3: Functions
Examples:
You cannot have 2 answers for the same multiple choice problem.

17. Lesson 3: Functions
Examples:
You cannot have 2 answers for the same multiple choice problem.
You cannot have 2 “y’s” for the same “x”. x = 1y (from A Function Song)

18. Lesson 4: Vertical Line Test
Use the vertical line test to identify graphs in which y is a function of x.
A. B.

19. Lesson 5: To Be or Not to Be
Determine whether the relation is a function.
{(1, 2), (3, 4), (5, 6), (5, 8)}
{(1, 2), (3, 4), (6, 5), (8, 5)}

20. 1.2(a): Do I Get It? Yes or No
1. Find the domain and range of the relation. Deter-mine whether the relation is a function.
{(1, 2), (3, 4), (6, 5), (8, 5)}
2. Use the graph to the right to
identify the domain and range.
Use the vertical line test to
identify the graphs below in
which y is a function of x.
A. B.

21. Yes, a function because no elements in the range have the same domain.
1.2(a): Do I Get It? Yes or No
Answers:
1. Domain: {1, 3, 6, 8}; Range: {2, 4, 5}
Yes, a function because no elements in the range have the same domain.
2. Domain: {x|-3 < x < 3} or [-3,3]; Range: {y|-3 < y < 1} or [-3,1]
3. A. Yes, function; B. No, not a function