1. Deep and Wide: Domain & Range
TEKS A.2B The student is expected to identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete

2. A function is a set of ordered pairs of numbers (x, y) such that no x –values are repeated.
What are the domain and range of a function?
The domain and range of a function are sets that describe those ordered pairs.

3. Definition Example {(3, 6), (2, 8), (5, 3)} { 3, 2, 5} { 6, 8, 3}
Domain
All the x-coordinates in the function's ordered pairs
{ 3, 2, 5}
Range
All the y-coordinates in the function's ordered pairs
{ 6, 8, 3}

4. The domain is the set of all the values of the independent variable, the x-coordinate
The range is the set of all the values of the dependent variable, the y-coordinate.

5. Identify the domain and range of the function below.
{ 2, 7), (4, 11), (6, 15), (8, 19)}
The domain is { 2, 4, 6, 8}
The range is { 7, 11, 15, 19}

6. Graphs
The domain of a function is the set of all the x-coordinates in the functions’ graph
Domain ≤ x ≤ 12

7. The range of a function is the set of all the y-coordinates in the functions’ graph
Range 6 ≤ y ≤ 12

8. What is the domain of this function? What is the range of this function?
Domain is 0 ≤ x ≤ 4
Range is 1 ≤ y ≤ 5
Answer: Domain is 0 ≤ x ≤ 4
Range is 1 ≤ y ≤ 5

9. The graph shows the path of a golf ball
What is the range of this function?
F 0 < y < 100
G 0 ≤ y ≤ 100
H 0 ≤ x ≤ 5
J 0 ≤ x ≤ 5
Answer is G
Is this function continuous or discrete?
Would it be reasonable to have a range with negative numbers?

10. What is the domain of this function?
A -1 ≤ x ≤ 5
B ≤ x ≤ 9
C 2 ≤ x ≤ 5
D 0 ≤ y ≤ 9
Students should immediately realize that “D” cannot be the answer because y is the dependent variable and therefore y represents the RANGE, not the DOMAIN.
Answer is A

11. What is the domain of the function shown on the graph?
A -2 < y ≤ 2
B -4 ≤ x ≤ 6
C -4 < y ≤ 2
D -2 < x ≤ 6
Students should immediately realize that A and C cannot be the answer. We are looking for domain. Therefore, our variable will be an X, NOT A Y.

12. Sometimes you will be asked to determine a REASONABLE domain or range

13. The average daily high temperature for the month of May is represented by the function
t = 0.2n + 80
Where n is the date of the month. May has 31 days. What is a reasonable estimate of the domain?
Answer: 1 ≤ n ≤ 31
What is a reasonable estimate of the range
Answer: See next slide

14. Our function rule is: t = 0.2n + 80
Our domain is 1 ≤ n ≤ 31
Our smallest possible n is 1
Our largest possible n is 31
To find the range, substitute 1 into the equation and solve. Then substitute 31 into the equation and solve.

15. Our function rule is: t = 0.2n + 80
Substitute a 1
t = 0.2n + 80
t = 0.2(1) + 80
t =
t = 80.2
Substitute a 31
t = 0.2n + 80
t = 0.2(31) + 80
t =
t = 86.2
Reasonable range is ≤ t ≤ 86.2