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Let's break down the problem step by step.

The function given is:
\[
f(x) = 10x + 20
\]
where $x$ is the number of members on the team and $f(x)$ is the total cost in dollars for buying T-shirts for the team.

### Conditions:
- There are at least 9 members but no more than 17 members on the team. Hence, $x$ is constrained by:
  \[
  9 \leq x \leq 17
  \]
  
### Step 1: Finding the possible range for $f(x)$
For the given values of $x$ (from 9 to 17), we calculate the corresponding values of $f(x)$:

- When $x = 9$:
  \[
  f(9) = 10(9) + 20 = 90 + 20 = 110
  \]
  
- When $x = 17$:
  \[
  f(17) = 10(17) + 20 = 170 + 20 = 190
  \]

Thus, the range of $f(x)$ is:
\[
110 \leq f(x) \leq 190
\]

### Step 2: Analyzing the answer choices
1. **"The values of $x$ and $f(x)$ must both be whole numbers between 10 and 20."**
   - This is incorrect because the range of $x$ is between 9 and 17, and the range of $f(x)$ is between 110 and 190, not between 10 and 20.

2. **"The value of $x$ must be a whole number between 9 and 17 and the value of $f(x)$ must be a whole number between 110 and 190."**
   - This is correct. Based on the calculations, $x$ is constrained between 9 and 17, and $f(x)$ is constrained between 110 and 190.

3. **"The value of $x$ must be a whole number between 0 and 190 and the value of $f(x)$ must be a whole number between 0 and 17."**
   - This is incorrect because the range of $x$ is 9 to 17, not 0 to 190. Also, the range of $f(x)$ is 110 to 190, not 0 to 17.

4. **"The value of $x$ must be a whole number between 0 and 17 and the value of $f(x)$ must be a whole number between 0 and 190."**
   - This is incorrect because although the range of $x$ is between 9 and 17, the range of $f(x)$ starts from 110, not 0.

### Correct answer:
The second statement is the correct one:
- "The value of $x$ must be a whole number between 9 and 17 and the value of $f(x)$ must be a whole number between 110 and 190."

Would you like more details on this solution, or have any questions? Here are some related questions to explore further:

1. How would the function change if the cost per T-shirt was $15 instead of $10?
2. What happens to the range of $f(x)$ if the number of team members increases to a maximum of 20?
3. If the fixed cost (the constant term in the function) were increased, how would that affect $f(x)$?
4. Could the function $f(x)$ represent a scenario where the cost per T-shirt decreases as the number of team members increases?
5. What would be the result of evaluating $f(x)$ for non-integer values of $x$?

**Tip:** Always check the boundaries of your variables to ensure the solution meets all the constraints given in the problem.

A principal was buying T-shirts for her school's basketball team and found that the total cost in dollars could be found by the function f(x) = 10x + 20, where x is the number of members on the team. If there are at least 9 members on the team but not more than 17, then which of the following statements describes the function?

Learn how to interpret a linear function used to calculate the total cost of buying T-shirts for a basketball team. This problem explores the domain and range of f(x) = 10x + 20, constrained by the number of members on the team. Suitable for students in Grades 8-10.

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