Pearson Assessments



Math 382 Lesson

FOUNDFUN7

5 Days – May 20, 21, 22, 23, and 27, 2014

Domain and Range

|Enduring Understandings |

|The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. |

|The student understands that data representing real-world situations can be collected, organized, and interpreted in order to solve problems. |

|The student understands that functions can be used to model real-world situations. |

|Vocabulary |

|function, independent, dependent, discrete, continuous, domain, range, input, output, mapping, scatter plot |

|A.2B(R) The student uses the properties and attributes of functions. The student is expected to identify mathematical domains and ranges and determine |

|reasonable domain and range values for given situations, both continuous and discrete. |

|The student will know… |The student will be able to… |

|The domain represents the independent values (x-values) in|Identify domain and range from a graph, table, or set of ordered pairs. |

|a function. |Identify domain/range values given range/domain of a function. |

|The range represents the dependent values (y-values) in a |Identify an appropriate and reasonable domain and range for a given situation (emphasize |

|function. |verbal description and de-emphasize formal notation). |

|The difference between continuous data and discrete data. |Inequality notation |

|The domain and range of a function may be different from |The difference between ‘less than’ and ‘less than or equal to’ |

|the domain and range for a situation represented by that |The difference between ‘greater than’ and ‘greater than or equal to’ |

|function. |How to express the value of a number as a range (-2 < x < 3) |

| |Identify domain and range of a continuous or discrete situation. |

| |Ex 1: The cost of a food bill equals $2 per hamburger times the number of hamburgers ordered.|

| | |

| |For the function y = 2x, D={real #s} and R={real #s} and the graph of the function is a line |

| |(continuous). |

| |For the situation, the D={positive whole numbers} and R={2, 4, 6, 8,…} The graph shows points |

| |(1 , 2), (2 , 4), etc. (discrete). |

| |Ex 2: The perimeter of a rectangle is 12. Its area is represented by equation A = x(6 – x), |

| |where A is the area of the rectangle and x is the length of the rectangle. |

| |For the function A = x(6 – x), the D={real #s} and R={all numbers less than or equal to 9} |

| |(continuous). |

| |For the situation, D={all numbers between (but not including) 0 and 6}, and R={all whole |

| |numbers between 0 and 10} (continuous). |

Prior Knowledge

Students will have an understanding of functions and a working knowledge of independent, input, dependent, and output presented in FOUNDFUN1, FOUNDFUN2, FOUNDFUN3 and FOUNDFUN4.

Materials needed

• MATH_0382_FOUNDFUN7_LES_02

• MATH_0382_FOUNDFUN7_MAT_DOMRANG1_02 (Day 1)

• MATH_0382_FOUNDFUN7_MAT_DESCRIBEGRAPHACT_02 (Day 2)

• MATH_0382_FOUNDFUN7_MAT_DOMRANG2_02 (Day 2)

• MATH_0382_FOUNDFUN7_MAT_PUZZLERS_02

• MATH_0382_FOUNDFUN7_MAT_PUZZLERKEYS_02

• MATH_0382_FOUNDFUN7_MAT_DOMRANGUPALEVEL_02 (Day 4)

• MATH_0382_FOUNDFUN7_MAT_CONTDISCVOCAB_02 (Day 5)

• 1 half-page copy of Inequality Practice per student (Day 1)

• 1 copy of Describing Graphs recording sheet per group of 2 to 4 students—2 pages can be copied front to back (Day 2)

• 1 set of Describing Graphs cards copied on cardstock per group of 2 to 4 students. For each group, Cards A through D are cut apart and placed in one plastic bag and cards E through J are cut apart and placed in a second plastic bag. These are reused each class period. (Day 2)

• 1 pad of 2” x 2” sticky notes per group of students (Day 2)

• 1 Coordinate Grid Mat per group of students (located in same file as Puzzler #1 and #2 (Day 3)

• 1 set of Puzzler #1 cards copied on cardstock per group of 2 to 4 students, cut, and placed in a plastic bag. These are reused each class period. (Day 3)

• 1 set of Puzzler #2 cards copied on cardstock per group of 2 to 4 students, cut, and placed in a plastic bag. These are reused each class period. (Day 3)

• 1 copy of Puzzler #1 recording sheet per student—2 pages can be copied front to back (Day 3)

• 1 copy of Puzzler #2 recording sheet per student—2 pages can be copied front to back (Day 3)

• 1 copy of On Your Own: Domain and Range per student as an exit ticket (Day 3)

• 1 copy of the Taking Domain and Range to Another Level recording sheet per student (Day 4)

• 1 copy of Vocabulary Organizer recording sheet per student (Day 5)

• 1 copy of Information Cards per student (2 copies are on 1 page in the PDF) (Day 5)

• Tape or glue sticks (Day 5)

• Scissors (Day 5)

• 1 copy of the Domain and Range Match-Up cards copied on cardstock per group of 2 students, cut, and placed in a plastic bag. These cards are reused each class period. (Day 5)

• 1 copy of the Domain and Range Match-Up recording sheet per student (Day 5)

Procedure

Day 1

o Use the PowerPoint file MATH_0382_FOUNDFUN7_MAT_INTROTODOMRANG1_02

to present the lesson. Students will learn how to write inequality statements from situations and graphs in preparation to describe domain and range with linear inequalities. Be sure that when writing these inequalities, the < (less than) or < (less than or equal to) signs are used. Please do not allow students to use > (greater than) or > (greater than or equal to) signs as this will confuse them later in Algebra I.

o Inequality Practice is included with this file for classwork and/or homework.

Day 2

o Complete the Describing Graphs Discovery Activity with students in groups of 2 – 4. This activity requires students to discuss possible values of a function from a graph. Distribute one Describing Graphs recording sheet and one plastic bag of Describing Graphs cards A – D to each group. Graphs E – J will be used in the second half of the activity. Have students look at Graph A and use sticky notes to create a rectangular area to help them determine possible x- and y-values for the graph. This visually creates a boundary on which they can focus. See picture below.

o Ask students to state possible y-values for the table for Card A on the recording sheet. Once all the y-values have been completed for Card A, go through the three questions beneath the table on the recording sheet.

• What do the closed circles indicate? That the values represented are included.

• How could you describe the x-values that are graphed? Greater than or equal to -2 and less than or equal to 2 ([pic]). Accept either description (verbal or formal notation).

• How could you describe the y-values that are graphed? Greater than or equal to -3 and less than or equal to 3 ([pic]). Accept either description (verbal or formal notation)

o Listed below are some extension questions you can ask. These may help students understand that all the values between the two boundaries are included, including the boundary points, and not just the values listed in the table.

• If 1.5 were included in the table, what would be a possible y-value? Close to – 1.5

• If – 1.75 were included in the table, what would be a possible y-value? Close to – 2.75

• Are there other x-values included in the graph other than the ones listed in the table? Yes

• What are some of the other x-values shown on the graph of the function? Accept any number from – 2 to 2, inclusive.

o Have students complete the tables for Graphs B through D and describe possible x- and y-values for graphs of the functions either verbally or in formal notation. It is not necessary at this point to require students to write the descriptions in formal notation. While students are working on this part of the activity, circulate around the room checking their work.

o Once all the groups have finished Graphs A – D and described possible x- and y-values for graphs of the functions, distribute one plastic bag containing Cards E – J to each group. Have students turn their recording sheet over and answer the questions. This part of the activity requires students to compare the Graphs from A – D with the graphs from E – J to find common domains and ranges. Before students begin this part of the activity, go over the definition of domain and range (located at the top of the student recording sheet). At this point, you are simply formalizing the vocabulary. Notice that the questions include the description and formal vocabulary. (Which graph(s) have the same possible x-values (domain) as the graph on Card A?)

o Once groups have completed the questions, use the PowerPoint file MATH_0382_FOUNDFUN7_MAT_INTROTODOMRANG2_02 to present the lesson paying close attention to the teacher notes beneath each slide. (It would be best to print the slides with notes prior to class and have these notes in hand during the discussion.) Have groups check their work with other groups. Debrief the class about the activity. Once this is done, go through the presentation where domain and range are further discussed (synonyms) and then end the class with the practice provided at the end of the presentation. There are four graphs at the end of the presentation. Ask students to identify the domain and range of each graph. The answers are in the notes section of the PowerPoint presentation.

o Domain and Range Practice is included with this file for classwork and/or homework.

o Domain and Range Quiz is also included and is optional.

Day 3

o Pass out a Coordinate Grid Mat and a set of Puzzler #1 cards to each group of 2 to 4 students. Also pass out a copy of the Puzzler #1 recording sheet to each student. (Students do not need to cut out the cards as indicated in the first bullet on the recording sheet.) Students should find the graph cards that match the given domain and range and sketch the graph on their recording sheet. Students should also note the letter of the cards they used to make each graph.

o Next, hand each group of students the Puzzler #2 recording sheet and a set of Puzzler #2 cards. (Students do not need to cut out the cards as indicated in the first bullet on the recording sheet.) Students should find the graph cards that match the given domain and range and sketch the graph on their recording sheet. These graph cards do not have letters because they can be rotated.

o Students should complete the On Your Own: Domain and Range problems as an exit ticket.

Day 4

o Use the MATH_0382_FOUNDFUN7_MAT_DOMRANGUPALEVEL_02 SMART Notebook file to present the lesson. Students will record information on their recording document as the lesson discusses the difference between the domain and range with discrete and continuous data. The presentation begins with the equation y = 30 – 3x without a scenario, then poses a discrete scenario for this same equation, and finally poses a continuous scenario for the equation. Students should walk away with the understanding that the domain and range—and whether the data is continuous or discrete—depends upon the scenario given. It is not necessary to have students write the questions and answers on their recording documents for every question posed in the SMART Notebook file, but space is provided to write down important facts. The summary statements on slides 9, 17, 28, 29, and 30 are required, and fill-in-the-blank spaces are provided for these summary statements on the recording document.

o Three practice problems are provided for classwork after the SMART Board lesson or for classwork or homework.

Day 5

o As a quick recap of the lesson yesterday, students will cut out the small Information Cards and tape or glue them in the appropriate cells of the Vocabulary Organizer that compares discrete and continuous data. Students will also give an example of continuous data and explain why it is continuous at the bottom of the page.

o Students will complete the Domain and Range Match-Up activity. Scenarios and headings for tables of values are given on the recording sheet. Students will write the letter of the graph and record the domain and range from the cards in the appropriate row of the table. Students will also indicate if the data is discrete or continuous. Domains and Ranges on the cards are based on the graphs given.

o Taking Domain and Range to Another Level – Part 2 is provided for classwork and homework practice.

Inequality Practice

Match each description with the correct inequality.

_____1. all numbers less than or equal to – 4 A. [pic]

_____2. all numbers between – 4 and 8. B. [pic]

_____3. all numbers greater than 8 C. [pic]

_____4. all numbers greater than or equal to 4 D. [pic]

_____5. all numbers between 4 and 8, inclusive E. [pic]

_____6. all numbers between – 4 and 4 F. [pic]

_____7. all numbers less than 4 G. [pic]

_____8. all numbers greater than – 8 H. [pic]

_____9. all numbers between – 8 and 8, inclusive I. [pic]

_____10. all numbers greater than or equal to – 4 J. [pic]

Inequality Practice

Match each description with the correct inequality.

_____1. all numbers less than or equal to – 4 A. [pic]

_____2. all numbers between – 4 and 8. B. [pic]

_____3. all numbers greater than 8 C. [pic]

_____4. all numbers greater than or equal to 4 D. [pic]

_____5. all numbers between 4 and 8, inclusive E. [pic]

_____6. all numbers between – 4 and 4 F. [pic]

_____7. all numbers less than 4 G. [pic]

_____8. all numbers greater than – 8 H. [pic]

_____9. all numbers between – 8 and 8, inclusive I. [pic]

_____10. all numbers greater than or equal to – 4 J. [pic]

Inequality Practice – Answer Key

1. H

2. E

3. C

4. J

5. D

6. I

7. A

8. F

9. G

10. B

Domain and Range Practice

Find the domain and range for each graph.

1. 2.

Domain: Domain:

Range: Range:

3. 4.

Domain: Domain:

Range: Range:

____________________________________________________________________________________

5.

Domain:

Range:

6. 7.

Domain: Domain:

Range: Range:

8. 9.

Domain: Domain:

Range: Range:

10. Sketch a graph of a function with the following domain and range:

Domain: -3 < x < 2

Range: -1 < y < 4

Domain and Range

Daily Quiz

Domain and Range Practice – Answer Key

1. Domain: -4 < x < -1 OR all numbers between -4 and -1

Range: -1 < y < 3 OR all numbers between -1 and 3, including 3

2. Domain: -2 < x < 2 OR all numbers between -2 and 2, inclusive

Range: -4 < y < -2 OR all numbers between -4 and -2, inclusive

3. Domain: -4 < x < 1 OR all numbers between -4 and 1, inclusive

Range: 1 < y < 5 OR all numbers between 1 and 5, inclusive

4. Domain: x > 2 OR all numbers greater than 2

Range: y < 5 OR all numbers less than or equal to 5

5. Domain [pic] OR all numbers between 0 and 50, inclusive

Range [pic] OR all numbers between 0 and 100, inclusive

6. Domain: {-4, -2, 0, 2}

Range: {-3, -1, 1, 3}

7. Domain: [pic] OR all numbers between -2 and 6, inclusive

Range: [pic] OR all numbers between -2 and 2, inclusive

8. Domain: {1, 3, 5, 7, 9}

Range: {2, 6, 10, 14, 18}

9. Domain: x > -3 OR all numbers greater than -3

Range: y < 2 OR all numbers less than or equal to 2

10. Answers will vary, but the graph below shows a possible answer.

Domain and Range Quiz

Matching

Match each statement with the correct inequality notation. 10 points each

_____1. all numbers greater than or equal to 7 A. [pic]

_____2. all numbers between – 3 and 7, inclusive B. [pic]

_____3. all numbers between – 3 and 7 C. [pic]

_____4. all numbers less than – 3 D. [pic]

_____5. all numbers greater than – 3 E. [pic]

_____6. all numbers less than or equal to 7 F. [pic]

Comparing Graphs

Use the graphs below to answer questions 7 – 10. 7 points each

7. Which graphs have the same domain?_________________________________________________

8. Which graphs have the same range?__________________________________________________

9. Which graph(s) has a domain of [pic]?____________________________________________

10. Which graph(s) has a range of [pic]?______________________________________________

Domain and Range Quiz – Answer Key

1. D

2. B

3. E

4. A

5. F

6. C

7. B and D

8. A and D

9. C

10. B

Taking Domain and Range to Another Level – Part 1

Student Recording Sheet

Slides 1 through 9 – Look at the equation y = 30 – 3x.

Because there are _______________ _______________ ordered pairs that make the equation

y = 30 – 3x true, and the ordered pairs are connected with a _______________ line, we say that the data points for this equation are _______________ data.

Slides 10 through 17 - We attach a scenario to the equation y = 30 – 3x.

The data points for this scenario are _______________ data for the portion of the equation that relates to the scenario. That means that only _______________ ordered pairs can be graphed for the equation in Quadrant I, and the data is not connected with a _______________ line.

Slides 18 through 28 - We attach a scenario to the equation y = 30 – 3x.

The data points for this scenario are _______________ data for the portion of the equation that relates to the scenario. That means that the data points are connected with a _______________ line on the graph, and that line represents All _______________ Numbers in Quadrant I.

Slide 29 - Continuous Data vs. Discrete Data

Slide 30 – Questions to Ask About Domain and Range

1. What is the independent variable? Is it measured continuously (all values between ___ and ___)

or is it counted discretely (1, 2, 3, …)?

2. What is the dependent variable? Is it measured continuously (all values between ___ and ___)

or is it counted discretely (1, 2, 3, …)?

3. If I were to graph this data, would I graph individual points (discrete data) or would I connect the

points with a line or line segment (continuous data)?

Caution: Discrete data can be counted with fractions and decimals! Read the situation carefully!

Taking Domain and Range to Another Level Part 1 Practice Problems

1. Skylar received a gift card to Moondollar Coffee Shop with an initial balance of $35. Every time she makes a purchase with the card, she buys a cappuccino that costs $3.50, including tax. Complete the table below to show the balance on the gift card after each cappuccino purchased.

|Number of Cappuccinos |Balance Left on Gift Card|

|Purchased |y |

|x | |

|0 | |

|1 | |

|2 | |

|3 | |

|4 | |

|5 | |

|6 | |

|7 | |

|8 | |

|9 | |

|10 | |

a. What equation can be used to represent this scenario?

b. Graph the data for this scenario. Be sure to label each axis of the graph.

c. Should the points be connected? Why or why not?

d. Is the data for this scenario continuous or discrete? How do you know?

e. Write the domain and range for this scenario.

D =

R =

2. Create a table of values for the equation y = 2x + 5. Then graph the equation.

a. Should the points on the graph of this equation be connected? Why or why not?

b. Is the data for this scenario continuous or discrete? How do you know?

c. Write the domain and range of the equation, y = 2x + 5.

D =

R =

3. On his 720-mile trip to Oklahoma City, Michael travels at a constant rate of 60 miles per hour. The equation y = 60x can be used to represent this situation. Complete the table below to show the distance traveled after each hour of the trip.

|Number of Hours |Total Distance Traveled |

|x |y |

|1 | |

|2 | |

|3 | |

|4 | |

|5 | |

|6 | |

|7 | |

|8 | |

a. What equation can be used to represent this scenario?

b. Graph the data for this scenario. Be sure to label each axis of the graph.

c. Should the points be connected? Why or why not?

d. Is the data for this scenario continuous or discrete? How do you know?

e. How many hours will it take Michael to complete his trip? How do you know?

f. Write the domain and range for this scenario.

D =

R =

Taking Domain and Range to Another Level Part 1 Practice Problems

Answer Key

1.

a. y = 35 – 3.5x

b.

c. No, because she cannot buy parts of cappuccinos or have increments of money other than multiples of $3.50.

d. Discrete, because cappuccinos and money are counted and the points on the graph are not connected.

e. D = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

R = {0, 3.5, 7, 10.5, 14, 17.5, 21, 24.5, 28, 31.5, 35}

2.

a. Yes, because there is no scenario to limit the values of x and y.

b. Continuous, because any Real Number makes the equation true.

c. D = {All Real Numbers}

R ={All Real Numbers}

3.

a. y = 60x

b.

c. Yes, because time is being measured continuously.

d. Continuous, because the data can be measured at any time—not just on the hour.

e. 12 hours; When time is 12 hours, the distance is 720 miles. I found this on my calculator.

f. D = {x| 0 < x < 12}

R = {y| 0 < y < 720}

|Scenario |Graph |Domain, Range and Type of Data |

|[pic] | |Domain: |

| | |Range: |

| | |Discrete or Continuous (Circle One) |

|[pic] | |Domain: |

| | |Range: |

| | |Discrete or Continuous (Circle One) |

|[pic] | |Domain: |

| | |Range: |

| | |Discrete or Continuous (Circle One) |

|[pic] | |Domain: |

| | |Range: |

| | |Discrete or Continuous (Circle One) |

|[pic] | |Domain: |

| | |Range: |

| | |Discrete or Continuous (Circle One) |

|A |B |

|C |D |

|E |D = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} |

|R = {0, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500} |R = {y| 90 < y < 140} |

|D = {x|0 < x < 20} |R = {0, 2.5, 5, 7.5, 10, 12.5, 15, 17.5, 20, 22.5, 25, 27.5, 30, 32.5, 35, 37.5, |

| |40} |

|D = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16} |R = {25, 27.50, 30, 32.50, 35, 37.50, 40, 42.50, 45, 47.50, 50} |

|R = {y|45 < y < 90} |D = {x|0 < x < 900} |

|D = {0, 2.5, 5, 7.5, 10, 12.5, 15, 17.5, 20, 22.5, 25} |This card is intentionally left blank. |

|Scenario |Graph |Domain, Range and Type of Data |

|[pic] |C[pic] |Domain: |

| | |D = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} |

| | |Range: |

| | |R = {25, 27.50, 30, 32.50, 35, 37.50, 40, 42.50, 45, 47.50, 50} |

| | |Discrete or Continuous (Circle One) |

|[pic] |D[pic] |Domain: |

| | |D = {x|0 < x < 20} |

| | |Range: |

| | |R = {y| 90 < y < 140} |

| | |Discrete or Continuous (Circle One) |

|[pic] |A[pic] |Domain: |

| | |D = {x|0 < x < 900} |

| | |Range: |

| | |R = {y|45 < y < 90} |

| | |Discrete or Continuous (Circle One) |

|[pic] |B[pic] |Domain: |

| | |D = {0, 2.5, 5, 7.5, 10, 12.5, 15, 17.5, 20, 22.5, 25} |

| | |Range: |

| | |R = {0, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500} |

| | |Discrete or Continuous (Circle One) |

|[pic] |E[pic] |Domain: |

| | |D = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16} |

| | |Range: |

| | |R = {0, 2.5, 5, 7.5, 10, 12.5, 15, 17.5, 20, 22.5, 25, 27.5, 30, 32.5, 35, 37.5,|

| | |40} |

| | |Discrete or Continuous (Circle One) |

Taking Domain and Range to Another Level – Part 2

Read each statement and decide if the graph of the data collected would be discrete or continuous. Think about the numbers you would use for the domain and range to help you make your choice. Circle your answer and write a short statement to justify it.

1. The number of emails a teacher receives in a given day

Discrete or Continuous

2. Height of a bean sprout as it grows

Discrete or Continuous

3. The number of cartons of milk in the school cafeteria

Discrete or Continuous

4. A person’s age from birth to age 80

Discrete or Continuous

5. Number of eggs a chicken produces in a week

Discrete or Continuous

6. Weight of a child from birth to 10 years of age

Discrete or Continuous

7. Ounces of juice in a drink dispenser

Discrete or Continuous

8. The function y = 15x represents the total cost in dollars, y, for a number of tickets purchased, x, at the Museum of Natural Science in Houston, Texas. Graph the function using a domain of 0, 1, 2, 3, and 4.

a. Should the points be connected on the graph?

Why or why not?

b. Is the data discrete or continuous?

How do you know?

c. Write the domain and range for this scenario.

D =

R =

9. Matt is working at the local fast food restaurant and earns $7.50 per hour. His employer has a policy of rounding up work hours to the nearest half hour. The following table shows amounts of money he may earn by working a particular number of hours per week.

|Hours Worked |Money Earned |

|1 |$7.50 |

|2 |$15 |

|3 |$22.50 |

|4 |$30 |

|5 |$37.50 |

|6 |45 |

|7 |$52.50 |

|8 |60 |

a. Graph the data for this scenario. Be sure to label each axis of the graph.

b. Should the points be connected? Why or why not?

c. Is the data for this scenario continuous or discrete? How do you know?

d. Write the domain and range for this scenario using data in the table above.

D =

R =

e. Graph the equation y = 7.5x at right. Use your

calculator to help you generate values for x and y.

f. Should the points on the graph of this equation be

connected? Why or why not?

g. Is the data for this equation continuous or discrete?

How do you know?

h. Describe the domain and range of the equation,

y = 7.5x.

D =

R =

10. Renee’s bathtub is completely filled with 80 gallons of water. The drain is leaking at a rate of 1 gallon every 2 hours.

|Hours |Gallons Remaining |

|0 |80 |

|10 |75 |

|20 |70 |

|30 |65 |

|40 |60 |

|50 |55 |

|60 |50 |

|70 |45 |

|80 |40 |

a. Graph the data for this scenario. Be sure to label each axis of the graph.

b. Should the points be connected? Why or why not?

c. Is the data for this scenario continuous or discrete? How do you know?

d. When will the bathtub be empty? (Hint: Use your calculator to help you!)

e. Write the reasonable domain and range for this scenario using the values on your calculator.

D =

R =

f. Graph the equation y = 80 – 0.5x on your graphing calculator. Why does the graphing calculator

connect all the ordered pairs with a solid line?

g. Is the data for this equation on the calculator continuous or discrete? How do you know?

h. Describe the domain and range of the equation y = 7.5x.

D =

R =

11. A car rental agency charges a one-time deposit of $55, plus a daily fee of $27 to rent a car. If this is represented by a function, where the rental cost, y, depends on the number of days, x, that the car is rented, which value below is reasonable for the range?

A $27

B $135

C $244

D $137

12. Jan is adding water to her swimming pool. She uses the equation y = 25 + 5x to represent the gallons of water in the pool, y, after x minutes. If Jan’s pool holds 5, 025 gallons of water, which of the following could be the domain of the function?

A D = {all real numbers}

B D = {x | 25 < x < 5025}

C D = {x | 0 < x < 1000}

D D = {x | x < 1000}

13. What is the range of the function shown below?

A R = {y | -7 < y < 8}

B R = {-7, -2, 8}

C R = {-8, -3, 0, 7}

D R = {y | -8 < y < 7}

14. Which graph shows a function with a domain of all real numbers greater than -2?

A C

B D

Taking Domain and Range to Another Level Part 2 - Answer Key

1. Discrete

2. Continuous

3. Discrete

4. Continuous

5. Discrete

6. Continuous

7. Continuous

8. a. No, because you can only purchase whole numbers of tickets and pay increments of $15.

b. Discrete, because you cannot buy parts of tickets.

c. D = {0, 1, 2, 3, 4}, R = {0, 15, 30, 45, 60}

9. a.

b. No, because hours are only counted in wholes and halves and money is only counted in

increments of $7.50.

c. Discrete, because you cannot have increments of hours other than wholes and halves.

d. D = {1, 2, 3, 4, 5, 6, 7, 8}, R = {7.5, 15, 22.5, 30, 37.5, 45, 52.5, 60}

e.

f. Yes, there is no scenario to limit the values for x and y.

g. Continuous, because values for x and y can be all Real Numbers that make this equation true.

h. D = {All Real Numbers}, R = {All Real Numbers}

10. a.

b. Yes, because the water is leaking at a constant rate and time can be counted in any increment.

c. Continuous, because, according to the table and graph given, any value between 0 and 80 makes

sense for the hours and any value between 40 and 80 makes sense for the gallons remaining.

d. At 160 hours, the bathtub will be empty.

e. D = {x|0 < x < 160}, R = {y| 0 < y < 80}

f. The graphing calculator makes every equation continuous unless you graph specific ordered pairs.

g. Continuous, because values for x and y can be all Real Numbers that make this equation true. There is no scenario to limit the values for x and y.

h. D = {All Real Numbers}, R = {All Real Numbers}

11. C

12. C

13. B

14. D

-----------------------

Discrete data is usually_______________—

as in the number of slushies or number of people. Discrete data includes only the points that make sense for the _______________ given. We graph discrete data with _______________ ordered pairs and do not connect the points.

Continuous data is usually measured continually—like _______________, _______________, or temperature. Continuous data includes _______________ the points in between any two ordered pairs. We graph continuous linear data with a _______________ line or line segment.

-7

-2

8

-8

-3

0

7

Graph A

Graph D

Graph C

Graph B

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