Question

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Explanation:

Identify variables

Using the Independent and Dependent Variables knowledge point

• Independent variable: speed (measured in mi/hr), as it is the controlled input.
• Dependent variable: stopping distance (measured in ft), as it depends on the speed of the vehicle.

Determine domain

Using the Domain and Range knowledge point

• The domain consists of the input values (speed): \(\{10, 20, 30, 40, 50, 60, 70\}\).
• Minimum value: \(10\)
• Maximum value: \(70\)

Determine range

Using the Domain and Range knowledge point

• The range consists of the output values (stopping distance): \(\{10, 38, 74, 120, 169, 234, 324\}\).
• Minimum value: \(10\)
• Maximum value: \(324\)

Select the correct graph

Using the Function Representation knowledge point

• The independent variable (speed) is plotted on the horizontal axis (x-axis), ranging from \(0\) to \(80\).
• The dependent variable (stopping distance) is plotted on the vertical axis (y-axis), ranging from \(0\) to \(350\).
• The data points show a curve that bends upwards (quadratic growth), starting at \((10, 10)\) and rising to \((70, 324)\).
• Graph C correctly displays speed on the horizontal axis, stopping distance on the vertical axis, and a curve bending upwards.

Describe the function in words

• As speed increases, the stopping distance increases at an increasing rate (the gap between consecutive stopping distances grows larger: \(28, 36, 46, 49, 65, 90\)).
• Thus, stopping distance grows faster as speed increases.

Answer:

Question 1

• The independent variable is speed and the dependent variable is stopping distance.
• The domain of the function consists of speed values. The minimum value of the domain is 10 and the maximum value of the domain is 70.
• The range of the function consists of stopping distance values. The minimum value of the range is 10 and the maximum value of the range is 324.

Question 2

• A. Graph with distance on the vertical axis showing a downward trend
• B. Graph with distance on the vertical axis showing a linear trend
• C. Graph with distance on the vertical axis showing an upward-curving trend (Correct answer)
• D. Graph with speed on the vertical axis

Question 3

• A. The rate at which stopping distance increases grows faster as speed increases. (Correct answer)
• B. The rate at which stopping distance increases remains constant as speed increases.
• C. The rate at which stopping distance increases grows slower as speed increases.