Given the piece-wise defined function: f(x)={2x−8 x<0 2x−16 x≥0 Calculate the following values: f(−1)= f(0)= f(2)=

The given piecewise-defined function is:

\[
f(x) = 
\begin{cases} 
2x - 8 & \text{if } x < 0 \\
2x - 16 & \text{if } x \geq 0 
\end{cases}
\]

We need to calculate \( f(-1) \), \( f(0) \), and \( f(2) \).

1. **For \( f(-1) \):**
   Since \( -1 < 0 \), we use the first piece of the function:
   \[
   f(-1) = 2(-1) - 8 = -2 - 8 = -10
   \]

2. **For \( f(0) \):**
   Since \( 0 \geq 0 \), we use the second piece of the function:
   \[
   f(0) = 2(0) - 16 = 0 - 16 = -16
   \]

3. **For \( f(2) \):**
   Since \( 2 \geq 0 \), we use the second piece of the function:
   \[
   f(2) = 2(2) - 16 = 4 - 16 = -12
   \]

### Summary of the values:
- \( f(-1) = -10 \)
- \( f(0) = -16 \)
- \( f(2) = -12 \)

Would you like more details or have any questions?

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Here are 5 related questions for further exploration:
1. How would the graph of this piecewise function look like?
2. What is the domain and range of this function?
3. What is the slope of the function in each interval?
4. Can you find the x-intercepts of each piece of the function?
5. What happens to the function as \( x \) approaches infinity?

**Tip:** When dealing with piecewise functions, always carefully check which part of the function applies to the value of \( x \) you're working with.

Learn how to calculate values for the piecewise function f(x) = { 2x - 8 if x < 0, 2x - 16 if x >= 0 }. Calculate f(-1), f(0), and f(2) with detailed step-by-step solutions. Suitable for students in Grades 10-12.

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