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Enduring Skill 1:

Students will develop an understanding of the concept of a function and use functions to describe quantitative relationships.

Demonstrators and Related Standards:

1. Understand that a function is a rule that assigns each input one output. (8.F.1; 8.F.3)

2. Understand that function is a description of a situation where one quantity determines another. (8.F.3; 8.SP.2)

3. Translate among different representations and partial representations of functions. (8.F.2; 8.F.4; 8.SP.3; 8.EE.5)

4. Describe how the qualitative features of a function are reflected in different representations of linear and non-linear functions. (8.F.2; 8.F.3; 8.F.4; 8.F.5; 8.SP.2; 8.SP.3; 8.EE.5)

Assessment Items:

• 1. ES 1, Demonstrator 1, Standard (8.F.1; 8.F.3)

Each of the four items below represent a relationship between x and y. Determine which relations represent a function.

I. II. {(-2,5) (-1,0) (0,-3) (2,5)}

III. IV.

a. I. and II b. I. II. and III. c. II. and III. d. All of the above e. None of the above

2. ES 1, Demonstrator 1, Standard (8.F.1; 8.F.3)

Fill in the following function table based on the given rule.

Rule: 𝑦 = 6𝑥 − 3

x y

-1

2

-15

15

6

X Y -1 0

0 4

0 -6

2 7

3

4

5

6

2

4

6

8

• 3. ES 1, Demonstrator 1, Standard (8.F.1; 8.F.3)

Which set of ordered pairs represents a function?

A. (-3,2), (-1,2), (0,-1), (2,4) B. (-2,6), (-3,4), (-3,2), (-4,0) C. (11,37), (8,28), (-7,31), (8,19) D. (2,18), (-3,12), (0,9), (2,6)

4. ES 1, Demonstrator 1, Standard (8.F.1; 8.F.3)

The relationship between the length of the sides of a square (s) and its perimeter (P) can be modeled by the function P = 4s. Find the missing measurements in the table below. Finally, identify the dependent and independent variables.

5. ES 1, Demonstrator 2, Standard (8.F.3; 8.SP.2)

Brad is going to order new jerseys for his soccer team. The jerseys will have the team logo printed on the front. Brad receives quotes from 2 companies:

Sports Gear Prints charges \$22 for each jersey and Graphic Designs and Prints charges a one time \$50 setup fee plus \$16.

a. Using n for the total number of jerseys ordered and c for the total cost create an equation that Brad can use for each company.

b. Brad needs to order 25 jerseys for his team. Using your equations from part a, determine which company will be the cheapest.

Side Length (s) Perimeter (P)

1 4

2 8

6 ?

9.25 ?

• 6. ES 1, Demonstrator 2, Standard (8.F.3; 8.SP.2)

What ONE thing in this function tells you it will be nonlinear.

𝑦 = 𝑥2 + 3𝑥 − 10

a. There are two terms containing x b. The first term containing x has a power of 2 c. There is one term that is constant d. There are three terms

7. ES 1, Demonstrator 2, Standard (8.F.3; 8.SP.2)

Which of the following equations is not a linear function?

a. y = .5x + 2

b. y = 𝑥2 c. y = 2x d. y = x - 2

• 8. ES 1, Demonstrator 2, Standard (8.F.3; 8.SP.2)

Jackson, Sarah and Evan walked 20 minutes to Lake Lots of Fish to go fishing. Each caught fish at a constant rate throughout the day. The fish Jackson caught is represented by the graph shown below. The fish Sarah caught is represented by the table below. The fish Evan caught is represented by the equation below.

a. Who caught fish at the faster rate?

b. How many fish does each person have at 5 hours?

Sarah’s Fish

Hours Spent Fishing Fish Caught

0 0

1 2

2 4

3 6

Evan’s Fish

f = 3h

• 9. ES 1, Demonstrator 2, Standard (8.F.3; 8.SP.2)

Which function contains all the values of x and y in the table?

10. ES 1, Demonstrator 2, Standard (8.F.3; 8.SP.2)

Jared wants to take his MP3 player and video game player on a car trip. One hour before they leave, he realizes that he forgot to charge the batteries of each device. At that point, he plugs in both devices so they can charge for the full hour before they leave.

His video game player is new so he does not know how fast it is charging, but he recorded the battery charge for the first 30 minutes after he plugged it in.

The rate in which his MP3 player chargers and its starting charge is given in the

following equation: 𝑐 = 12

15 𝑡 + 40

Which device(s) will be fully charged when they are ready to leave in one hour?

a. The MP3 player b. The video game player c. Both devices d. Neither devices

A y = - 3x + 1

B y = - 2x + 3

C y = - 3x – 2

D y = - 4x – 1

• 11. ES 1, Demonstrator 2, Standard (8.F.3; 8.SP.2)

Kobe earns extra money by giving tennis lessons to elementary age students. He charges the students a one time fee of \$25 and then \$11 per hour. Kobe earned \$74.50 last week. How many hours did he give lessons last week?

12. ES 1, Demonstrator 2, Standard (8.F.3; 8.SP.2)

For school trips, a local water park charges a flat rate plus an additional rate for each student. The water park uses a linear function to determine the total cost in dollars (y) if x students attend the field trip. The following table shows a partial representation of this function.

Water Park Field Trip Cost

Number of Students (x) 1 2 3 4 5

Total cost in Dollars (y) 43 46 49 52 55

A. What is the rate of change represented by the table and what does it represent in the problem? Show your work and explain your answer. B. The first x-value in the table is 1. Explain why it is more appropriate for the

table to start at x = 1 instead of x = 0.

13. ES 1, Demonstrator 2, Standard (8.F.3; 8.SP.2)

Brauck and Forrest both have a pet snake. They both believed what they feed their snake would make it grow the fastest. They begin measuring their snakes weekly to determine which diet is the best. The table below shows the growth of Brauck’s snake over several weeks.

Number of Weeks (x) 0 1 2 3 4

Length in Centimeters (y) 12.8 13.2 13.6 14.0 14.4

The equation y = 11.2 + 0.5x represents, y, the length in centimeters, of Forrest’s snake over x days. Which statement accurately compare the growth of the plants?

A. Brauck’s snake is growing at a faster rate than Forrest’s snake. B. Forrest’s snake is growing at a faster rate than Brauck’s snake. C. Both snakes are growing at the same rate. D. Forrest’s snake was growing at a faster rate than Brauck’s at first, but then Brauck’s snake began to grow at a faster rate.

• 14. ES 1 Demonstrator 4, Standard (8.F.3; 8.F.2)

The table below shows the relationship between the side length of a square and the area of a square.

Side Length

1 2 3 4 5

Area 1 4 9 16 25

A. Create a graph to represent the relationship between the side length of a square and the area of the square. B. Determine if the relationship between side length and area is linear or non-linear.

C. How does the table show the relationship is linear or non-linear? D. How does the graph show the relationship is linear or non-linear?

15. ES 1 Demonstrator 4, Standard (8.F.3; 8.F.2)

Ashley walks from her home to a park at a constant rate, watches a ball game and then walks home at the same constant rate.

Which graph matches the description of Ashley’s walk?

a. b.

c. d.

• 16. ES 1 Demonstrator 4, Standard (8.F.3; 8.F.2)

Determine the rate of change and initial value of the given table. x y

1 0

2 2

3 4

4 6

5 8

Rate of Change: __________________

Initial Value: ______________________

17. ES 1 Demonstrator 4, Standard (8.F.3; 8.F.2)

Identify each of the following functions as linear or non-linear.

A. 𝑦 = 2𝑥2 + 3𝑥 − 5 B. C.

D. E. y = 3x + 2 F.

• 18. ES 1 Demonstrator 4, Standard (8.F.3; 8.F.2)

Which of the following does NOT accurately describe the given graph?

A. The graph has two increasing intervals, one decreasing interval, and one constant interval.

B. The graph begins and ends with an interval increasing. C. The third interval of the graph is decreasing. D. Each increasing interval is followed by a constant interval.