Question

Let f(x) be the function that gives the average cost per book in dollars when using an online store to print x copies of a self-published paperback book. Use the graph of f(x) = 120 + 4x to answer the following questions. What does the end behavior of the function say about the context?

A. The cost increases as x increases.
B. The cost decreases as x increases.
C. The cost remains constant as x increases.
D. The function doesn't provide information about the context.

Answer 1

The end behavior of the function indicates that the cost per book increases as the number of copies increases.

Step-by-step explanation:

The end behavior of the function says that as the number of copies of the book increases, the average cost per book increases. This is because the function is given by f(x) = 120 + 4x, where x represents the number of copies. The constant term 120 represents the fixed cost, and the coefficient of x, which is 4 in this case, represents the cost per book. Since the coefficient of x is positive, it means that the cost per book increases as the number of copies increases.

a. To predict the cost for a textbook with 400 pages, we substitute x = 400 into the function. f(400) = 120 + 4(400) = 120 + 1600 = 1720 dollars.

b. To predict the cost for a textbook with 600 pages, we substitute x = 600 into the function. f(600) = 120 + 4(600) = 120 + 2400 = 2520 dollars.

3. To sketch the regression line, you would need the actual data points to perform a regression analysis. Without the data points, it is not possible to sketch the regression line based solely on the equation of the function.