Question

1. a large pizza costs $13.99 and each additional topping costs $1.25.

a) define the variables (tell me what it stands for, dont give me a number)
b) write a function f to represent the situation.
c) using the function you created in part b, find the cost of a large pizza with three toppings.
d) what does f(0) mean in the context of the problem.
e) how many toppings are on a pizza that costs $20.24

Explanation:

Step1: Define variables

Let \( x \) be the number of additional toppings. Let \( f(x) \) be the total cost of the pizza.

Step2: Write the function

The base cost is \( 13.99 \) and each topping costs \( 1.25 \). So the function is \( f(x)=13.99 + 1.25x \).

Step3: Find cost for 3 toppings

Substitute \( x = 3 \) into \( f(x) \).
\( f(3)=13.99+1.25\times3=13.99 + 3.75=17.74 \).

Step4: Interpret \( f(0) \)

Substitute \( x = 0 \) into \( f(x) \). \( f(0)=13.99+1.25\times0 = 13.99 \). It means the cost of a large pizza with no additional toppings.

Step5: Find number of toppings for \( f(x)=20.24 \)

Set \( f(x)=20.24 \), so \( 20.24=13.99 + 1.25x \).
Subtract \( 13.99 \) from both sides: \( 20.24-13.99=1.25x \), \( 6.25 = 1.25x \).
Divide both sides by \( 1.25 \): \( x=\frac{6.25}{1.25}=5 \).

Answer:

a) \( x \): number of additional toppings; \( f(x) \): total cost of pizza.
b) \( f(x)=13.99 + 1.25x \).
c) \( 17.74 \).
d) Cost of a large pizza with no additional toppings.
e) \( 5 \).