Question

A bowling alley charges $4 to rent shoes and $2.75 per game. As part of a promotion, the alley lowers the price of shoes to $3. What kind of transformation describes the change in the total cost of bowling x games per person?

a. Translation
b. Rotation
c. Reflection
d. Dilation

Answer 1

The promotion at the bowling alley represents a translation transformation on the cost function, as it shifts the total cost downward by $1 without changing the cost per game slope.

Step-by-step explanation:

The change in the total cost of bowling x games per person, due to the reduction in the price of shoes from $4 to $3, is a translation. This is because the reduction in the shoe rental price simply shifts the cost function downward by $1, without altering the slope of the cost function that represents the cost per game. In mathematical terms, if the original cost function was C(x) = 4 + 2.75x (where C represents the total cost and x represents the number of games played), the new cost function after the promotion would be C'(x) = 3 + 2.75x. This represents a vertical shift downward of the line on a graph by $1 for every x, which is characteristic of a translation.