Sure, let's solve the problem step-by-step.
We are given that the price of a pizza is [tex]$\$[/tex] 7.99[tex]$ plus an additional $[/tex]\[tex]$ 1.35$[/tex] for each topping.
First, we need to write a function rule that gives the total price as a function of the number of toppings, [tex]$x$[/tex]. We can express the total price [tex]$f(x)$[/tex] as follows:
[tex]\[
f(x) = 7.99 + 1.35x
\][/tex]
where [tex]$x$[/tex] is the number of toppings.
Now, we need to calculate the values of this function for given [tex]$x$[/tex] values:
1. For [tex]$x = 0$[/tex] (0 toppings):
[tex]\[
f(0) = 7.99 + 1.35(0) = 7.99
\][/tex]
2. For [tex]$x = 1$[/tex] (1 topping):
[tex]\[
f(1) = 7.99 + 1.35(1) = 7.99 + 1.35 = 9.34
\][/tex]
3. For [tex]$x = 2$[/tex] (2 toppings):
[tex]\[
f(2) = 7.99 + 1.35(2) = 7.99 + 2.70 = 10.69
\][/tex]
4. For [tex]$x = 6$[/tex] (6 toppings):
[tex]\[
f(6) = 7.99 + 1.35(6) = 7.99 + 8.10 = 16.09 \quad (\text{Note: correction from the table provided})
\][/tex]
5. For [tex]$x = 10$[/tex] (10 toppings):
[tex]\[
f(10) = 7.99 + 1.35(10) = 7.99 + 13.50 = 21.49
\][/tex]
So, the prices for each number of toppings in the table are derived as follows:
\begin{tabular}{|c|c|}
\hline number of toppings [tex]$(x)$[/tex] & price [tex]$f(x)$[/tex] \\
\hline 0 & 7.99 \\
\hline 1 & 9.34 \\
\hline 2 & 10.69 \\
\hline 6 & 16.09 (corrected) \\
\hline 10 & 21.49 \\
\hline
\end{tabular}
The function rule [tex]\( f \)[/tex] that gives the total price as a function of the number of toppings [tex]\( x \)[/tex] is:
[tex]\[
f(x) = 7.99 + 1.35x
\][/tex]
