an international calling plan charges 45 cents per minute or fraction of a minute for each call. which graph…

an international calling plan charges 45 cents per minute or fraction of a minute for each call. which graph models the cost, y, in cents of making x minutes of international calls?

an international calling plan charges 45 cents per minute or fraction of a minute for each call. which graph models the cost, y, in cents of making x minutes of international calls?

Answer

Explanation:

Step1: Analyze the cost function

The cost ( y ) (in cents) for ( x ) minutes of calls is a step - function because it charges 45 cents per minute or fraction of a minute. For ( 0 < x\leq1 ), ( y = 45 ); for ( 1 < x\leq2 ), ( y=45 + 45=90 ); for ( 2 < x\leq3 ), ( y = 90+45 = 135 ), and so on. In general, ( y=\lceil x\rceil\times45 ), where ( \lceil x\rceil ) is the ceiling function (the smallest integer greater than or equal to ( x )).

Step2: Check the y - axis scale

The first two graphs have a y - axis with a maximum value of 54, which is too small because for ( x = 8 ) minutes, the cost should be ( 8\times45=360 ) cents. The third graph has a y - axis that can accommodate values up to 450, which is appropriate. Let's check the points:

  • For ( x = 1 ) (or ( 0 < x\leq1 )), ( y = 45 ) (open circle at ( x = 0 ), closed circle at ( x = 1 ) for ( y = 45 )).
  • For ( x = 2 ) (or ( 1 < x\leq2 )), ( y=90 ) (open circle at ( x = 1 ), closed circle at ( x = 2 ) for ( y = 90 )).
  • For ( x = 3 ) (or ( 2 < x\leq3 )), ( y = 135 ) and so on. The third graph (the one with y - axis labels 45, 90, 135, 180, 225, 270, 315, 360, 405, 450) matches these values. The first two graphs have incorrect y - axis scaling (their y - axis is too small to represent the cost for 8 minutes which is ( 8\times45 = 360 ) cents).

Answer:

The third graph (the one with y - axis values 45, 90, 135, 180, 225, 270, 315, 360, 405, 450 and x - axis from 0 to 8 minutes)