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 time interval (−9, 7).

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

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

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

Answer 1

Given:

The function f represents the diver's distance from sea level over time, in seconds.

`f(x)=\begin{cases}3x+1 & \text{ if } -9<x\leq -2 \\ -5 & \text{ if } -2<x\leq 1 \\ x-6 & \text{ if } 1<x<7 \end{cases}`

To find:

The correct statement for the domain.

Solution:

Domain is the set of input values for which the function is defined.

Here, x values are the input values and they represent time intervals on which the function is defined

Here, the possible intervals for x are
`-9<x\leq -2,-2<x\leq 1,1<x<7`.

`Domain=(-9,-2]\cup (-2,1]\cup (1,7)`

`Domain=(-9,7)`

Therefore, the domain is the time interval (−9, 7). Hence the correct option is A.