https://file.aiquickdraw.com/mathbot/file/1729818839064thtekru7.jpg

We are asked to find \( f(7) \) from the given piecewise function:

\[
f(x) =
\begin{cases} 
-2x + 3 & \text{if } x < 1 \\
4x - 3 & \text{if } 1 \leq x \leq 9 \\
-6x + 3 & \text{if } x > 9 
\end{cases}
\]

Since \( 7 \) falls within the interval \( 1 \leq x \leq 9 \), we use the corresponding piece of the function:

\[
f(x) = 4x - 3
\]

Substituting \( x = 7 \):

\[
f(7) = 4(7) - 3 = 28 - 3 = 25
\]

Thus, \( f(7) = 25 \).

Would you like further details or have any questions?

Here are five related questions for further exploration:
1. What is \( f(0) \) for this piecewise function?
2. What is \( f(10) \) for this piecewise function?
3. How do you graph a piecewise function like this one?
4. What is the domain of the function \( f(x) \)?
5. How would you evaluate \( f(x) \) if \( x = 1 \)?

**Tip**: Always check which interval your value of \( x \) falls into before applying the corresponding function rule.

Find f(7) for this piecewise-defined function: f(x) = -2x + 3 if x < 1, 4x - 3 if 1 ≤ x ≤ 9, -6x + 3 if x > 9. Write your answer as an integer or as a fraction in simplest form.

Learn how to evaluate f(7) for a given piecewise-defined function. This problem involves piecewise functions and basic algebraic substitution. Suitable for students in Grades 8-10.

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