Question

The number of rows in a movie theater can be represented by the function f(x)=12x. The number of seats in each row in the theater can be represented by the function g(x)=x+9. Which function represents the total number of seats, h(x)=f(x)×g(x)?

A) h(x)=12x+108
B) h(x)=12x²+180
C) h(x)=12x−108
D) h(x)=12x²+108

Answer 1

The total number of seats in the theater is represented by the function h(x) = 12x² + 108x, which is obtained by multiplying f(x) = 12x and g(x) = x + 9. The function h(x) represents the product of rows and seats per row.

Step-by-step explanation:

The student has presented functions representing the number of rows in a movie theater and the number of seats in each row. To find the function that represents the total number of seats in the theater, we multiply the two functions together, f(x) = 12x representing the rows, and g(x) = x + 9 representing seats in each row. Multiplying these two gives h(x) = f(x) × g(x) = 12x × (x + 9) = 12x² + 108x.

Therefore, the correct function that represents the total number of seats in the theater is h(x) = 12x² + 108x. None of the given options matches this function exactly, so there might be an error in the provided options. If the student is required to choose from the options provided, none are correct and clarification from the instructor may be necessary.