Question

A scuba diver returning to the surface swims to move up quickly, then waits a few meters below the surface to avoid pressure issues. They complete the ascent more slowly. The function f represents the diver's distance from sea level over time, in seconds. Which of the following is true for f? f(x)= { 3x+1, if −9 < x ≤ −2 f(x)= {−5, if. −2 < x ≤ 1 f(x)= { x−6, if 1 < x < 7 Group of answer choices The domain is the depth interval (−26, 1). The domain is the depth interval (−9, 1]. The domain is the set of times −9 < x < −2, −2 < x < 1, and 1 < x < 7. The domain is the time interval (−9, 7). Group of answer choices domain: (–3, 3] negative: (–3, –2), (2, 5] range: (–3, 4] decreasing: (–1, 4) increasing: (–3, –1) positive: (–2, 2)

Answer 1

See below

Explanation:

Given:

• f(x)= { 3x+1, if −9 < x ≤ −2
• f(x)= {−5, if. −2 < x ≤ 1
• f(x)= { x−6, if 1 < x < 7

Combination of domain for the function is the following union:

• (-9, 2]∪ (-2, 1]∪(1, 7) = (-9, 7)

Group of answer choices:

The domain is the depth interval (−26, 1).

• incorrect as (-26, -9) interval is not covered in given function

The domain is the depth interval (−9, 1].

• incomplete range

The domain is the set of times −9 < x < −2, −2 < x < 1, and 1 < x < 7.

• incorrect as doesn't include x = -2 and x = 1

The domain is the time interval (−9, 7).

• This is correct as it is same with the domain set we got above.