Algebraic Reasoning Unit 2 Test Review

What is the average rate of change for the data set given below?

• 4.5

• 4.8

• 5.3

• 24

Answer explanation

To find the average rate of change, calculate the difference between the maximum and minimum values in the data set, then divide by the number of intervals. The correct average rate of change is 4.8.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Look at the table below. Which of the following best represents the function model for f(x) generated by using the average rate of change?

• f(x) = 4.4x + 44

• f(x) = 5.5x + 10

• f(x) = 5.5x + 54

• f(x) = 4.4x + 10

Answer explanation

The average rate of change calculated from the table leads to the slope of 5.5. The y-intercept is determined to be 10, making the correct function model f(x) = 5.5x + 10.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Look at the table below. If the function model for this table is f(x) = -7.6x + 116, which of the following best describes the accuracy of the function model for data values when x is equal to 6, 10, and 14?

• The function model f(x) provides a fairly accurate estimate of the values in the data set. The function model f(x) overestimates the value of f(x) for x equal to 6, 8, and 10.

• The function model f(x) provides a fairly accurate estimate of the values in the data set. The function model f(x) underestimates the value of f(x) for x equal to 6, 8, and 10.

• The function model f(x) does not provide an accurate estimate of the values in the data set.

• The function model f(x) is an exact match for the values in the data set.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Look at the table below. Which of the following is true about the domain and range of the data set and the function model for f(x)? I. The domain of the data set is {x | x = 1, 2, 3, 4, 5, 6}. II. The range of the data set is {f(x) | f(x) = 20, 22, 32, 40, 49, 60}. III. The domain of the function is {x | x ≥ 20}. IV. The range of the function is {f(x) | f(x) ∈ ℝ}.

• A. I and III

• B. I, III, and IV

• C. I, II, and III

• D. I, II, and IV

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

Look at the table below. Which of the following best represents the function model for f(x) generated by using the average rate of change?

• A. f(x) = 0.75x + 31

• B. f(x) = 1.4x + 31

• C. f(x) = 0.75x + 5

• D. f(x) = 1.4x + 5

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Look at the table below. Which of the following best represents the average finite difference?

• A. Δf(x)/Δx ≈ -0.05

• B. Δf(x)/Δx ≈ -19.2

• C. Δf(x)/Δx ≈ -1.85

• D. Δf(x)/Δx ≈ -0.54

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

The data below shows the cooling temperatures of a freshly brewed cup of coffee after it is poured from the brewing pot into a serving cup.

• 43.4%

• 0.434%

• 4.34%

• None of these

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Which of the following would represent the domain and range for the function on the question above over a 50 minute period?

• Domain: [0, ∞) Range: [100.5, 179.5]

• Domain: [0, ∞) Range: [0, 179.5]

• Domain: [0, 50] Range: [0, 179.5]

• Domain: [0, 50] Range: [100.5, 179.5]

The data below shows the cooling temperatures of a freshly brewed cup of coffee after it is poured from the brewing pot into a serving cup. Which of the following represents the restricted domain and range of the data set?

• A. Domain: {x | x ∈ R}

  Range {y | y ∈ R}

• B. Domain: {x | x = 179.5, 168.7, 158.1, 149.2, 141.7, 134.6, 125.4, 123.5, 116.3, 113.2, 109.1, 105.7, 102.2, 100.5}

  Range: {y | y = 0, 5, 8, 11, 15, 18, 22, 25, 30, 34, 38, 42, 45, 50}

• C. Domain: {x | 0 ≤ x ≤ 50}

  Range: {y | 100.5 ≤ y ≤ 179}

• D. Domain: {x | 100.5 ≤ x ≤ 179.5} Range: {y | 0 ≤ y ≤ 50}

A graph of the function f(x) = -0.25x - 1 is shown. According to the graph, what is the value of x when f(x) = 1?

• -8

• -1.5

• 4

• 1

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1