Question

An audio books club charges an initial joining fee of $20.00. The cost per audio book is $15.00. The graph shows the cost of belonging to the club as a function of audio books purchased. How will the graph change if the cost per audio book goes up by $1.00?

(The new function is shown by the dotted line.)

Answer 1

The new function will have a steeper slope, so...

Explanation:

Le: t x ----> the number of audio books purchased

y ---->the cost of belonging to the club in dollars

case 1 (Originally) :

y = 15x + 20

case 2 ( the cost per audio book goes up by $1.00) :

y= (15+1)x+ 20

y = 16x + 20

The slope of the new function is greater than the slope of the original function

The new function will have a steeper slope:

16 $/ audio book > 15 $/audio book

Answer 2

The graph will change by simply having an increased slope of 16 instead of 15.

Explanation:

For this problem, we will consider the initial case as stated by the problem where the joining fee is $20 and each book is $15. Let x represent the number of books that we have purchased. Then, we can write the following function to represent the cost of this club.

f(x) = 15x + 20

Note, if x = 0, meaning we have no books, then

f(0) = 15(0) + 20

f(0) = 0 + 20

f(0) = 20

Which is the cost of our joining fee. If x = 1, meaning we have 1 book, then

f(1) = 15(1) + 20

f(1) = 15 + 20

f(1) = 35

Which is the cost of our joining fee and 1 book, which matches our graphed function.

Now, let's consider that the cost of the book is $16 instead of $15 ("the cost per audio book goes up by $1.00"). Then we can modify the slope of our function to reflect this change giving us the new function:

g(x) = 16x + 20

In this new function, our slope increased from 15 to 16, to account for the increase in cost, but our initial 20 remained the same.

So the graph will change by simply having an increased slope of 16 instead of 15.

Cheers.