Question

The temperature of a pot of water placed on a hot burner can be found using the function f(x) = 25x + 60, where x is the number of minutes since the pot was placed on the burner. If the pot of water is on the burner for no more than 3 minutes, what is the domain of the function for this situation?

Answer 1

`0 \leq x \leq 3`

Explanation:

Given

`f(x) = 25x + 60`

Required

Determine the domain

The domain, in this case means the possible values of x

From the question, we understand that x represents minutes

Since it's impossible to have a negative minutes, then x starts at 0

i.e.
`x \geq 0` or
`0 \leq x`

Also, from the question, we understand that the time can not be more than 3 minutes

i.e.

`x \leq 3`

Now, we have two inequalities:

`0 \leq x` and
`x \leq 3`

Which can be written as:

`0 \leq x \leq 3`

Hence, the domain is:
`0 \leq x \leq 3`