Analyzing Functional Relationships

Question 1

The path of a basketball during a free throw can be modeled with the function shown, where x is time, in tenths of a second, since releasing the ball and f(x) represents height in feet. Which statements correctly describe this function?

Revolt · Accepted Answer

A: The basketball reaches a maximum height of 7 feet.; D: The height of the ball at time 0 is 6 feet.; E: The graph is symmetric about the line x = 5.5.

Question 2

A projectile’s motion is modeled by the function given in the table, where x represents time in seconds and f(x) represents height above the ground. At what time is the projectile on the ground?

Revolt · Accepted Answer

B: 2 seconds

Question 3

Marcus tracked the changes in his sales over a 12-month period and graphed the results. Over which interval was the change in Marcus’s sales constant?

Revolt · Accepted Answer

B: (0, 5)

Question 4

The growth of a strain of bacteria can be modeled by the function graphed, where the x-values are the time in seconds and the y-values are the number of bacteria. How many bacteria are there initially?

Revolt · Accepted Answer

B: 2.7

Question 5

A delivery up to 1 mile costs $10. For any distance over 1 mile, there is an additional charge at the rate of $5 per mile, with a limit of 5 miles. Which graph represents this scenario?

Revolt · Accepted Answer

C:

Question 6

A plant is 2 inches tall. In sunlight, the plant grows 1 inch each week. At the end of the 4th week, the plant is placed in a dark room for 2 weeks and stops growing. It is then returned to the sunlight and grows at the same rate for the next 3 weeks. Describe how you would go about sketching the graph of this relationship. Include key features of the graph in your description.

Revolt · Accepted Answer

To graph this relationship, I would plot the height on the y-axis and time in weeks on the x-axis. The y-intercept is (0, 2) because the plant starts at 2 inches. From x = 0 to x = 4, the graph is a line with a slope of 1, reaching a height of 6 inches. From x = 4 to x = 6, the plant stops growing, so the graph is a horizontal line at y = 6. From x = 6 to x = 9, the plant grows again at a slope of 1, ending at a maximum height of 9 inches at point (9, 9).

Question 7

a linearan absolute value✔ an exponentiala quadratic

Revolt · Accepted Answer

C: ✔ an exponential

Question 8

What did you include in your response? Check all that apply.

Revolt · Accepted Answer

A: y-intercept is at (0, 2); B: increasing on (0, 4) and (6, 9); C: constant on (4, 6); D: maximum at (9, 9)

Question 9

✔ decreases onlyincreases onlydecreases and then increasesincreases and then decreases

Revolt · Accepted Answer

A: ✔ decreases only

Question 10

The table shows the amount of a radioactive sample that remains after a certain number of days. Use the data in the table to describe the relationship between the number of milligrams remaining and days.

Revolt · Accepted Answer

The sample originally weighed mg.: 10; The relationship is best modeled by function that .: an exponential; The relationship is best modeled by function that .: decreases only

Analyzing Functional Relationships Answers

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