Algebra Review Help

Question

YOU HAVE 26 CDs and plan to buy 2 more each month. Write a rule for the number of Cds as a function of the number of months from now. Identify the independent and dependent variables, the domain, and the range.

Answer 1

Your function would be c = 26 + 2*m, where c is the number of CDs you will own after m months.

Why: you already own 26 CDs, so 26 + more. How many more? Well 2 per month, which means (+ 2) for each month, e.g. 26 + (2 + 2 + 2) after three months, better written as 26 + (2*3).

 

The domain and range of you function are unclear based on the wording of the question (that is, do you buy the CDs semi-monthly, regularly? Did you start your 26 CD collection with the same pattern of purchasing? etc...) But we can at least say the domain is the whole numbers (or natural numbers including 0, or the non-negative integers), i.e. {0, 1, 2, 3, ...}. And the range is the even numbers greater then or equal to 26, i.e. {26, 28, 30, 32, ...}.

Why: the domain is the set of values (i.e. all the values) the independent variable m can be, and the range is the set of values the dependent variable c can be, considering the domain. That is, the range is the set of values you get if you pass every value in the domain through the function (i.e. evaluate the function at every value in the domain.)

Answer 2

Let CD = the number of CDs and m = the number of months

 

CD = 2m + 26              [Start with 26, add 2 each month (m)]

 

Here's an input-output table:

 

m   CD

0    26

1    28

2    30

3    32

...    ...

 

m is the independent variable, CD is the dependent variable (it depends on m)

 

Domain is m≥0           [0,+∞)

The problem does not state what happened in the past when m<0

 

Range is CD≥26         [26,+∞)

The problem does not state what number of CDs you had in the past