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QUANTITIES AND RELATIONSHIPS: Skills Practice • 1

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I. Identifying Independent and Dependent Quantities

A. Determine the independent and dependent quantities in each scenario. Be sure to include the appropriate units of measure for each quantity.

1. Selena is driving to visit her grandmother who lives 325 miles away from Selena’s home. She travels an average of 60 miles per hour.

3. On her way to work each morning, Sophia purchases a small cup of coff ee for $4.25 from the coff ee shop.

5. Jose prefers to walk to work when the weather is nice. He walks the 1.5 miles to work at a speed of about 3 miles per hour.

2. Benjamin works at a printing company. He is making T-shirts for a high school volleyball team. The press he runs can imprint 3 T-shirts per minute with the school’s mascot.

4. Phillip enjoys rock climbing on the weekends. At some of the less challenging locations he can climb upwards of 12 feet per minute.

6. Gavin works for a skydiving company. Customers pay $200 per jump to skydive in tandem skydives with Gavin.

Skills PracticeName Date

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QUANTITIES AND RELATIONSHIPS

IM1_SP_M01_T01.indd 1IM1_SP_M01_T01.indd 1 24/05/18 11:23 AM24/05/18 11:23 AM

2 • MODULE 1: Searching for Patterns

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B. Label the axes of each graph with the independent and dependent quantities and the appropriate unit of measure.

1. Madison enjoys bicycling for exercise. Each Saturday she bikes a course she has mapped out around her town. She averages a speed of 12 miles per hour on her journey.

0

y

x

Distance Madison Bikes

2. Natasha is fi lling the bathtub with water in order to give her dog Buster a bath. The faucet fi lls the tub at an average rate of 12 gallons per minute.

0

y

x

Amount of Water in Bathtub

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Name Date

3. Marcus throws a football straight up into the air. After it reaches its maximum height of 20 feet, it descends back to the ground.

0

y

x

Football Height

4. Chloe is using a pump to drain her backyard pool to get ready for winter. The pump removes the water at an average rate of 15 gallons per minute.

0

y

x

Amount of Water in Pool

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II. Identifying Domain and Range

A. Identify the domain and range of each situation using words and inequalities.

1. Victoria recently switched to a new electric company. If she uses between 0 and 400 kilowatt-hours (kWh) of electricity per month, the cost is a set price of $30. If she uses 400 kWh or more per month, the price is $0.097 per kWh.

2. Rohan is at an amusement park. While waiting in line, he reads the statistics on the roller coaster he is about to board. The coaster reaches a maximum speed of 75 miles per hour, and the ride lasts three minutes.

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3. Graham uses a hot water bottle on an injury to his back he incurred playing basketball. He fi lls the bottle with water that is a temperature of 100°F. After 25 minutes, Graham fi nds that the bottle has cooled and he stops using it.

4. Lenore is going to sell T-shirts at a fi eld hockey game to raise money for the team. She fi nds a website that makes custom T-shirts. The company charges $11.99 per shirt for an order less than 50, $9.99 per shirt for 50 to 100 T-shirts, and $7.99 for more than 100 T-shirts.

5. A township buys a new asphalt road paver. The paver costs $50,500. The value of the paver decreases each year after purchase. Eventually, it decreases so much in value that it can only be sold for $2,500 for parts.

6. Peyton is training to run a half-marathon. One night, she runs a total of 10 miles. She runs the fi rst 4 miles at a pace of 6 miles per hour, the next 5 miles at a pace of 7 miles per hour, and the last mile at a pace of 4 miles per hour.



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III. Identifying Characteristics of Graphs

A. Sort the graphs into groups. Write the letter of the graph in the group box. (Some graphs belong to more than one group.)

1.

Function Maximum or Minimum Increasing Only Decreasing Only

−8 −6 −4 −2−2

−4

20 4 6 8

Graph A

−8

−6

8

6

4

2

y

x−8 −6 −4 −2

−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

Graph B

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−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

Graph C

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

Graph D

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

Graph E

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

Graph F

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−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

Graph K

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

Graph L

IV. Identifying Functions

A. Determine which relations represent functions. If the relation is not a function, state why not.

1.

Domain Range

25 8

22 10

0 8

6 15

2.

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

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Name Date

3. y 5 x224 4.

–4

–1

0

3

2

7

11

14

5.

Domain Range

2 4

7 3

2 0

3 7

6.

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

Topic 1




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B. Rewrite each function using function notation.

1. Rewrite the function y 5 3x 2 8 using function notation so that the dependent quantity, defi ned as f, is a function of the independent quantity x.

3. Rewrite the function y 5 3x 1 8 using function notation so that the dependent quantity, defi ned as P, is a function of the independent quantity x.

5. Rewrite the function d 5 2 1 __ 2 m 1 5 using function notation so that the dependent quantity, defi ned as A, is a function of the independent quantity m.

2. Rewrite the function y 5 23x2 1 6x 2 1 using function notation so that the dependent quantity, defi ned as C, is a function of the independent quantity x.

4. Rewrite the function l 5 |n 2 2| using function notation so that the dependent quantity, defi ned as L, is a function of the independent quantity n.

6. Rewrite the function c 5 2pr2 using function notation so that the dependent quantity, defi ned as C, is a function of the independent quantity r.

V. Recognizing Function Families

A. Determine whether each graph represents a linear function, a quadratic function, an exponential function, a linear absolute value function, or a linear piecewise function.1.

y

x

2. y

x

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Name Date

VI. Identifying Function Characteristics

A. Create an equation and sketch a graph for a function with each set of given characteristics. Use values that are any real numbers between −10 and 10.

1. Create an equation and sketch a graph that:

• is a smooth curve, • is continuous, • has a minimum, and • is quadratic.

−16 −12 −8 −4−4

−8

40 8 12 16

−16

−12

16

12

8

4

y

x

2. Create an equation and sketch a graph that:

• is linear, • is discrete, and • is decreasing across the entire domain.

−16 −12 −8 −4−4

−8

40 8 12 16

−16

−12

16

12

8

4

y

x

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