Question

A cell phone company $500 for a new phone and $60 for a monthly plan. If C(t) is a rational function that represents the average monthly cost of owning the cell phone, what is the range of the function?
A. R: (0,500)
B. R: (60,560)
C. R: R
C: R: (-infinity, infinity)

HOW DO I SOLVE THIS?!

Answer 1

The range of a function is the set of possible values that can be obtained from the dependent variable. The range of the function is: $R: (500, \infty)$

Given that:

$Phone = \ 500$

$Monthly\ Plan = \ 60$

Let the number of months be t. So, the function C(t) is calculated as follows:

$C(t) = Phone + Monthly\ Plan \times t$

$C(t) = 500 + 60 \times t$

$C(t) = 500 + 60t$

The range is calculated as follows:

The smallest possible value of t is 0 i.e. when no monthly subscription is done.

So, we have:

$C(0) = 500 + 60\times 0= 500 + 0 = 500$

And the highest is $\infty$ i.e. for a large value of t

So, we have:

$C(\infty) = 500 + 60\times \infty= 500 + \infty = \infty$

Hence, the range of the function is:

$R: (500, \infty)$

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