3C Domain and Range
Domain: x’s
Range: y’s
Realistic/Practical Domain: x values that make sense
Realistic/Practical Range: y values that make sense
Values that you can count: D: {all possible x’s}
R: {all possible y’s}
Ex: Jack has $2.00 in quarters and dimes. Let x represent the quarters.
D:{0,2,4,6,8} R:{0,5,10,15,20} because he can have (0 quarters, 8 dimes);
(2 quarters, 15 dimes); (4 quarters and 10 dimes); (6 quarters and 5 dimes); (8
quarters and 0 dimes)
Given a graph: D:{all possible x’s} R: {all possible y’s} Usually use descriptions like All reals, x<6, 2<x<4, y<6
etc..
D: 1 < x < 3
R: 2 < y<5
D: All Real
R: y < 2
D: All Real
R: y > 1
D: All Real
R: {2}
D: All numbers between 0 and 6
R: All numbers between 0 and 4
Given an equation: Graph the equation and then give the domain and range based on the graph.
Ex: y = (x-3)2 + 1. The graph is:
D: All Reals R: y> 1
Given a situation: Find the minimum (usually zero) and maximum x. Then find the minimum and maximum y.
Ex: A caterer charges Jack $25 plus $5 per person. He is expecting between 10 and 30 people at his party.
10 people: 25+5(10)  $75
30 people: 25 + 5(30)  $175.
D: 10 < x < 30 (between 10 & 30); R: 75 < y < 175 (between 75 & 175)
0
5
10
15
20
25
30
3C Domain and Range Practice:
A
Domains:
Ranges:
B
2. x >-1
7. {1,3,5}
1. {0, 1, 2}
6. All reals
Match the Domains and Range of the following:
C
3. {2}
8. 1< y<4
D
E
4. All reals
9. All numbers less than or equal to 2
5. 0<x<3
10. 2<y<4
11-14: Find the domain and range of the following graphs
11.
12.
13.
14.
15-19: Graph the equations on your calculator. Sketch a graph on your paper. Then give the domain and range
15. y = 3
16. y = 3x – 2
17. y = x2 – 4
18. y = 2x
19. {(8,0),(6,3),(4,6),(2,9),(0,12) }
20-21: Sketch a graph on your paper that has the following domain and range
20. Domain: All reals. Range: y > 2
21. Domain: 2 < x < 4 Range: -1< y < 6
22-26: Find the maximum and minimum x and y values for the situation. Sketch a small graph. State the domain and range.
22.
The cab fare is given by the equation F= 4m + 10 where m is the number of miles. Find the domain and range if Kayla rode
8 miles in the cab.
23.
The cab fare is given by the equation F=3m + 8 where m is the number of miles. Find the practical domain and range if
Jackson spent $41 on his cab ride.
24.
Jack is having a birthday party and hopes to invite about 20 people. A caterer charges $40 plus $5 per person.
practical domain and range?
What is the
25.
Everyday, two new flowers appear in the garden. At the beginning, there were 6 flowers. Mrs. Smith looks at her garden 9
days later. (Let x represent the number of days.) What is the practical domain and range?
26.
A cab charges a flat fee of $4 and $3 per mile.
What is a practical domain and range if she rides 20 miles?
Answer the following questions:
27.
Jackson has $1.50 in quarters and dimes. Let x represent the number of quarters. What is the domain? What is the range?
28.
Mary has one-dollar bills and five-dollar bills in her purse. She has a total of $28. Let x represent the number of one-dollar
bills. Find the domain and range.
29.
Alan has $2.00 in her pocket consisting of quarters and dimes. Let x be all the dimes. Find the appropriate domain and
range.
30.
Bob has $.50 in his pocket consisting of nickels and pennies. Let x be all of the pennies. Find the appropriate domain and
range.
31.
Jack travels 40 feet per minute. He travels for 10 minute. Let x be the time (in exact minutes) and y be the total distance.
Find the appropriate range.
32.
During the football game Friday Tabor only scored touchdowns for 7 points and field goals for 3 points. The final score was
42 points. Let x represent the number of touchdowns. What is an appropriate domain and range to represent the score?
33.
Susie sells cookies. She sells them for $1.50 each. She paid $5 for supplies and made a total of 10 cookies. Let x represent
the amount of cookies and y represent her profit. What is the appropriate range for her cookie selling?
34.
Jackson sells lemonade for $2 per cup. He paid $10 for supplies to sell 15 cups. What is the practical range for the profit of
his lemonade selling?
35.
The cost of soda is $2.00 and the cost of candy is $1.50. You have $15.00 in your wallet. How much of each item can you
purchase?
36.
Tonya has $24. Each soda cost $2. What is a practical domain and range?
37.
On the unit test there are two types of questions. Multiple choice questions are worth 3 points and free response questions
are worth 4 points. If Jacob made an 80, what are possible combinations of correct answers?