Question

A cell phone company charges by the minute (and partial minute) for a phone call. Arionna’s plan includes 300 minutes in the $20 base cost. If she uses more than 300 minutes, there is a $5 overage fee and an additional charge of $0.25 per minute. Which graph represents the cost of her plan per minute, where x represents the minutes used and y represents the cost?
A B C D

Answer 1

D, or the last graph on the bottom right. The line have to be connected for it to be the line in the question

Answer 2

Answer: First Graph A will be the correct graph for given function.

Explanation: Since, According to the given questions there are two conditions

1- Arionna’s plan includes 300 minutes in the $20 base cost.

That is, function f(x) =20, when $0\leq x \leq 300$

2- If she uses more than 300 minutes, there is a $5 overage fee and an additional charge of $0.25 per minute.

That is, function f(x)= 20+5+0.25x ⇒ f(x)= 25+0.25x, when x>300

Thus, we can say that there is a piece wise function of the entire given situation.

Which is $f(x)= \begin{cases}20 & \text{ if } 0\leq x\leq 300 \\ 25+.25x & \text{ if } x> 300 \end{cases}$

Since, after mapping the graph of above situation we found that It is similar to option A.

Note: according to graph B there is no charge for minutes less than 300 which is wrong. So, it can not be the graph of given situation.

In graph C until completing 300 minutes the charge is continuously increasing. But according to question it is fixed to 20 dollar. So, it can not be the graph of given situation.

In graph D except charge of per minute there is no overage fee for more than 300 minutes. which is also wrong.So, it can not be the graph of given situation.