Question

Math on the Spot A pizzeria charges $10 for a large cheese pizza plus $0.50

f(x)
per topping. The total charge for a pizza with x toppings is given by the function
= 0.50x + 10. Describe how the following changes affect the graph.
A. The cheese pizza's cost is increased to $14.
B. The charge per topping is raised to $1.00.

Answer 1

The cost increase of a cheese pizza causes a vertical shift upward on the graph, while an increase in charge per topping steepens the slope of the graph.

Step-by-step explanation:

The student's question involves determining how changes in the cost of cheese pizza and the charge per topping affect the graph of the function that represents the total charge for a pizza with x toppings. Originally, the function given is f(x) = 0.50x + 10, where x is the number of toppings.

A. If the cheese pizza's cost is increased to $14, this would change the function to f(x) = 0.50x + 14. On the graph, this shift would represent a vertical shift upwards by $4 since the base cost of the pizza (without toppings) has increased.

B. If the charge per topping is raised to $1.00, the new function would be f(x) = 1.00x + 10. On the graph, this would steepen the slope of the line, indicating that the total cost increases more rapidly with each additional topping.