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The problem asks which function matches the table. Let's solve it step by step.

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### Table:
- **Number of Days Rented (x):** 1, 2, 3, 4
- **Rental Cost (f(x)) in dollars:** 12, 17, 22, 27

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### Identify the pattern:
- **Difference between consecutive rental costs:**
  - $17 - 12 = 5$
  - $22 - 17 = 5$
  - $27 - 22 = 5$

This indicates a constant rate of **$5 increase per day**. So, the function likely follows the form:
\[
f(x) = 5x + b
\]
where $b$ is the initial rental cost for 0 days.

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### Finding the equation:
From the table:
- When $x = 1$, $f(1) = 12$.
Using the equation $f(x) = 5x + b$:
\[
12 = 5(1) + b \implies 12 = 5 + b \implies b = 7
\]
Thus, the function becomes:
\[
f(x) = 5x + 7
\]

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### Checking the Options:
- Option C: $f(x) = 7 + 5x$ matches our function, so **C is the correct answer**.

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Would you like further details on this solution, or do you have any follow-up questions?  

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Here are **5 related questions** to explore:  
1. What kind of functions show constant growth rates?  
2. How do you determine a function from a table?  
3. What would the equation look like if the rental cost started at $15 instead?  
4. How do linear functions compare to quadratic ones?  
5. How can you graph the function $f(x) = 7 + 5x$?

**Tip:** When dealing with tables, always check for a pattern by calculating the difference between consecutive outputs.

Which function matches the table? The table shows the number of days rented and corresponding rental costs as follows: Days Rented: 1, 2, 3, 4; Rental Cost: $12, $17, $22, $27. Four options are provided: A) f(x) = 5x, B) f(x) = 5 + 5x, C) f(x) = 7 + 5x, D) f(x) = 12 + 5x.

Learn how to match a function to a table showing rental costs. This problem covers linear functions and arithmetic sequences. We solve by identifying the rate of change and finding the correct linear equation. Suitable for students in Grades 6-8.

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