Modeling with Functions

Question 1

Explain why an inverse variation function is not the best model for the data set.

Revolt · Accepted Answer

An inverse variation function is not the best model for this data set because in an inverse variation, as x increases, y should decrease. In this data set, as x increases, y also increases. Additionally, for an inverse variation, the product of x and y (xy = k) should be constant. Here, (165)(198) = 32,670 and (170)(204) = 34,680. Since these products are not the same, the data does not represent an inverse variation.

Question 2

Explain what type of function is the best model for the data set and justify your choice.

Revolt · Accepted Answer

A linear function is the best model for this data set. The ratio of y to x for the ordered pairs is constant, meaning the relationship is a direct variation, which is a type of linear function. Additionally, when the data set is plotted on a graph, the points form a straight line.

Question 3

What is the slope of the linear function that models the data in the table?The slope is .

Revolt · Accepted Answer

1.2

Question 4

Explain what the slope and y-intercept of the linear model represent in the context of the situation.

Revolt · Accepted Answer

The slope of the linear model is 1.2, which represents Alberto's stride length in meters per step; for every additional step per minute, his speed increases by 1.2 meters per minute. The y-intercept is 0, which means that when his stride rate is 0 steps per minute, his speed is 0 meters per minute.

Question 5

meters per minute

Revolt · Accepted Answer

216

Question 6

What stride rate would Alberto need in order to match Usain Bolt’s speed in the 100-meter race?

Revolt · Accepted Answer

B: 516 steps per minute

Question 7

Which did you include in your response?

Revolt · Accepted Answer

A: The products of corresponding x- and y-values of an inverse variation function are constant.; B: As x increases, y also increases.; C: The product of coordinate pairs are not equal: (165)(198) = 32,670 and (170)(204) = 34,680.

Question 8

Which did you include in your response?

Revolt · Accepted Answer

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Question 9

What is the equation of the linear function that models the data in the table?

Revolt · Accepted Answer

A: y = 1.2x

Question 10

Which did you include in your response?

Revolt · Accepted Answer

A: The slope is 1.2.; B: The slope indicates that Alberto’s stride length is 1.2 meters per step.; C: The y-intercept is 0.; D: The y-intercept indicates that Alberto’s speed is 0 meters per minute when his stride rate is 0 steps per minute.

Modeling with Functions Answers

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