Question

A bucket has a leak that started 6 hours ago. At time 0, when the bucket just emptied, a tap was turned on for 3 hours. The amount of water in the bucket can be modeled by the function f(x) = |x| over the interval [−6, 3], where x is the time, in hours, and y is the amount of water in the bucket, in gallons. Which translation of the graph represents the last 3 hours of the leak, and the tap running for 6 hours? Group of answer choices g(x) = |x − 3| g(x) = |x| + 3 g(x) = |x| − 3 g(x) = |x + 3|

Answer 1

Answer:

The answer is g(x) = |x - 3|

Step-by-step explanation:

Answer 2

Here we have a general problem of horizontal translations, we will see that the correct option is g(x) = |x - 3|

We know that the bucket was leaking for 6 hours, and then it was filled in 3 hours.

Then in the interval [-6, 0) the bucket was leaking

In the interval [0, 3] the bucket was being filled.

Now we want a transformation that represents the last 3 hours of leaking.

Also, remember that for a general function f(x), an horizontal translation of N units is written as:

g(x) = f(x + N)

If N is positive, the translation is to the left

If N is negative, the translation is to the right.

If we want to represent the last 3 hours of leaking (which happen for negative values of x) then we need to move the whole graph to the right.

So, if we define the function as:

g(x) = f(x - 3)

when we evaluate g(x) in zero we get:

g(0) = f(-3)

So this new function, at the time zero, starts representing the last 3 hours of leaking of the bucket.

Remembering that f(x) = |x|

We can see that the correct option is:

g(x) = f(x - 3) = |x - 3|

g(x) = |x - 3|

Below you can see a graph with a comparison of f(x) and g(x), where the green one is f(x) and the blue one g(x).

If you want to learn more, you can read:

https://brainly.com/question/13435754