Question

A) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over times, x measured in seconds. During what interval(s) of the domain is the water balloon's height staying the same?
A.0 ≤ x ≤ 2

B.2 ≤ x ≤ 5

C.5 ≤ x ≤ 6

D.6 ≤ x ≤ 8


B) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. During what interval(s) of the domain is the water balloon's height increasing?

A.0 ≤ x ≤ 2

B.40 ≤ y ≤ 70

C.5 ≤ x ≤ 8

D.40 ≤ y ≤ 10


C) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. During what interval(s) of the domain is the water balloon's height decreasing the fastest?

A.5 ≤ x ≤ 9.5

B.8 ≤ x ≤ 9.5

C.6 ≤ x ≤ 8

D.5 ≤ x ≤ 6


D) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. Justify your answer from Part C.

A.5 ≤ x ≤ 9.5 is the interval where the balloon's height is decreasing.

B.8 ≤ x ≤ 9.5 is the interval where the slope is the steepest.

C.6 ≤ x ≤ 8 is the interval where the balloon's height decreases the most.

D.5 ≤ x ≤ 6 is the interval where the slope is the steepest.


Please help as fast as possible <3

Answer 1

From the given linear function, we have that:

A. The function is constant on the following interval: B.2 ≤ x ≤ 5.

B. The function is increasing on the following interval: A.0 ≤ x ≤ 2.

C. The function is decreasing the fastest on the following interval: D.5 ≤ x ≤ 6.

D. The justification for the previous item is: D.5 ≤ x ≤ 6 is the interval where the slope is the steepest.

When a function is constant?

A function is constant when it's graph is an horizontal line, hence in this problem the function is constant for two intervals.

• 2 ≤ x ≤ 5.

• 10 ≤ x ≤ ∞.

Hence, in item A, option B is correct.

When a function is increasing?

A function is increasing on the intervals that y is increasing while x increases, that is, the function is moving right and up.

Hence, in item B, option A is correct.

When a function is decreasing?

A function is decreasing on the intervals that y is decreasing while x increases, that is, the function is moving right and down.

The decrease is faster when the division of the change in the output by the change in the input has the lower value(greater absolute negative).

Hence:

• In item 3, option D is correct.

• In item 4, option D is correct.

More can be learned about linear functions at brainly.com/question/24808124

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