https://file.aiquickdraw.com/mathbot/file/1726709101660kl67izs6.jpg

The given function \( f(x) \) is a piecewise function:

\[
f(x) = \begin{cases} 
-(x + 6)^2 + 1 & \text{for } x \neq -4, \\
1 & \text{for } x = -4.
\end{cases}
\]

We are tasked with finding \( f(-9) \).

Since \( -9 \neq -4 \), we use the first piece of the function:

\[
f(x) = -(x + 6)^2 + 1.
\]

Now, substitute \( x = -9 \) into the equation:

\[
f(-9) = -((-9 + 6)^2) + 1 = -((-3)^2) + 1 = -(9) + 1 = -9 + 1 = -8.
\]

Thus, \( f(-9) = -8 \).

Would you like a further breakdown, or any other questions answered?

Here are five related questions for practice:
1. What is \( f(-4) \)?
2. What is \( f(0) \)?
3. How would the result change if \( f(x) \) was defined differently for \( x = -9 \)?
4. How does the graph of this piecewise function look for \( x \neq -4 \)?
5. How would you approach the problem if the second part of the piecewise function was more complex?

**Tip:** When dealing with piecewise functions, always check which condition the input value satisfies before applying a specific formula!

Find f(-9) for the piecewise function: f(x) = { -(x + 6)^2 + 1 for x ≠ -4, 1 for x = -4 }

Learn how to evaluate a piecewise function with quadratic terms by finding f(-9). The problem explores concepts like quadratic expressions and function substitution, suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation