Question

a child starts a piggy bank with $2. each day, the child receives 25 cents at the end of the day and puts it in the bank. if A represents the amount of money and d represents for the number of days then A(d)=2+0.25d gives the amount of money in the bank as a function of days. a)explain why the domain does not contain the value d=2.5. b)explain why the range does not include the value A=$3.10

Answer 1

For a given function f(x), the domain is the set of possible values of x that we can use and the range is the set of the possible values of f(x).

For both points we will find that the answer is:

"We only can evaluate the function with integer values of d."

a) Here we have the function:

A(d) = 2 + 0.25*d

The first thing we want to answer is:

"explain why the domain does not contain the value d=2.5 "

We know that at the end of each day the kids get's the $0.25, so at d= 2.5 there two days and a half, and because only 2 nights passed, at this moment the kid only got the money two times.

So for d = 2.1

           d = 2.5

           d = 2.7

etc

We would get the exact same total money, thus we only can evaluate the function with integer values of d.

b) Why the range does not include the value A = $3.10?

Remember that d can only be an integer number.

Now let's solve:

A(d) = 3.10 = 2 + 0.25*d

          3.10 - 2 = 0.25*d

          1.10 = 0.25*d

           1.10/0.25 = d = 4.4

So we only can get  A = $3.10 if d = 4.4, and remember that d only can be a whole number, this is why the range does not include the value $3.10

If you want to learn more, you can read:

brainly.com/question/1632425