The problem you're working on asks you to evaluate the function $f(x) = 25x + 200$, which represents the monthly cost of a cell phone plan, where $x$ is the number of phones on the plan. You are tasked with finding $f(3)$ and $f(5)$, and interpreting the results.

1. Finding $f(3)$:

To find $f(3)$, substitute $x = 3$ into the function:

$f(3) = 25(3) + 200 = 75 + 200 = 275$

Thus, $f(3) = 275$, meaning the monthly cost for a plan with 3 phones is $275.

2. Finding $f(5)$:

Next, to find $f(5)$, substitute $x = 5$ into the function:

$f(5) = 25(5) + 200 = 125 + 200 = 325$

Thus, $f(5) = 325$, meaning the monthly cost for a plan with 5 phones is $325.

Interpretations:

• $f(3) = 275$ indicates the cost of a cell phone plan with 3 phones is $275 per month.
• $f(5) = 325$ indicates the cost of a cell phone plan with 5 phones is $325 per month.

Would you like more details or have any further questions?

Here are 5 related questions to deepen your understanding:

1. What is the fixed cost in this pricing model?
2. How would the monthly cost change if the number of phones doubled from 3 to 6?
3. What does the coefficient of 25 represent in the equation $f(x) = 25x + 200$?
4. If the company increased the cost per phone by $5, what would the new function look like?
5. How much more expensive is a plan with 5 phones compared to a plan with 3 phones?

Tip: When working with linear functions, the coefficient of $x$ (in this case, 25) represents the rate of change per unit increase in $x$, such as the cost per additional phone.