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Given the following piecewise function,

f(−7)=
Blank 1 Question 22

f(−1)=
Blank 2 Question 22

f(0)=
Blank 3 Question 22

The piecewise function is defined as follows:

\[
f(x) = \begin{cases} 
3x - 1, & \text{if } x \geq -1 \\
-5, & \text{if } x < -1 
\end{cases}
\]

Let's evaluate the function for the given values of \( x \):

1. **\( f(-7) \):**

   Since \( -7 < -1 \), we use the second piece of the function:
   \[
   f(-7) = -5
   \]

2. **\( f(-1) \):**

   Since \( -1 \geq -1 \), we use the first piece of the function:
   \[
   f(-1) = 3(-1) - 1 = -3 - 1 = -4
   \]

3. **\( f(0) \):**

   Since \( 0 \geq -1 \), we use the first piece of the function:
   \[
   f(0) = 3(0) - 1 = 0 - 1 = -1
   \]

So, the values are:

\[
\begin{align*}
f(-7) &= -5 \\
f(-1) &= -4 \\
f(0) &= -1
\end{align*}
\]

Would you like further details or have any questions?

Here are 5 questions related to this topic:

1. How do you determine which part of a piecewise function to use?
2. What is the significance of the inequality in a piecewise function?
3. How would the function change if the condition was \( x > -1 \) instead of \( x \geq -1 \)?
4. What are the key differences between continuous and discontinuous piecewise functions?
5. How would you graph this piecewise function?

**Tip:** Always pay close attention to the inequality signs in piecewise functions to correctly determine which expression to use for evaluation.

Explore how to evaluate a piecewise function f(x) for specific values such as f(-7), f(-1), and f(0). This detailed explanation covers the concept of piecewise functions and demonstrates their application in mathematics. Suitable for students in Grades 9-12.

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