Question

A book club charges an initial joining fee of $18.00. The cost per book is $10.25. The graph shows the cost of belonging to the club as a function of books purchased. How will the graph change if the joining fee goes up by $3.00?

Answer 1

The question doesn't show any graph, but I have included it to help you with the problem.

Answer:

The new graph will be shifted up by 3 units

Step-by-step explanation:

Graph of a Real Function

The total cost of belonging to the book club depends on one fixed cost, the initial joining fee, and a variable cost, depending on the number of books purchased. Call C the total cost and x the number of purchased books, then

$C=18+10.25x$

By giving x some values, we get the corresponding values of C and then we can plot the graph as a blue line, in the image provided below.

If the joining fee goes up by $3, the new function is

$C'=18+10.25x+3$

$C'=21+10.25x$

The graph is also shown in the image, but with a red line. We can see the graph is shifted up by 3 units in the y-axis, but the slope remains the same, as the cost per book hasn't changed