Question

1. the function $f(x) = 2.75x + 16$ represents the cost, in dollars, of a large pizza with $x$ toppings. what does the 2.75 represent? type a response

Explanation:

Step1: Recall linear function form

A linear function is in the form \( f(x) = mx + b \), where \( m \) is the slope (rate of change) and \( b \) is the y - intercept (initial value).

Step2: Analyze the given function

In the function \( f(x)=2.75x + 16 \), which represents the cost of a large pizza with \( x \) toppings, we compare it to the linear function form. Here, \( x \) is the number of toppings. The coefficient of \( x \) (2.75) should represent the rate at which the cost changes with respect to the number of toppings. So, 2.75 represents the cost (in dollars) per topping. Because for each additional topping (increase in \( x \) by 1), the total cost \( f(x) \) increases by 2.75 dollars.

Answer:

The 2.75 represents the cost (in dollars) per pizza topping.