For the indicated​ function, find the values ​f(negative 4​), ​f(0​), and ​f(7​).
f left parenthesis x right parenthesis equals StartSet Start 2 By 1 Matrix 1st Row 1st Column x comma if x less than 0 2nd Row 1st Column 5 x plus 8 comma if x greater than or equals 0 EndMatrix

Question content area bottom
Part 1
​f(negative 4​)equals

enter your response here
Part 2
​f(0​)equals

enter your response here
Part 3
​f(7​)equals

enter your response here

To find the values of \( f(-4) \), \( f(0) \), and \( f(7) \) for the given piecewise function, we will evaluate the function based on the conditions provided:

\[
f(x) = \begin{cases} 
x, & \text{if } x < 0 \\
5x + 8, & \text{if } x \geq 0 
\end{cases}
\]

### Part 1: \( f(-4) \)
Since \( -4 \) is less than \( 0 \), we use the first part of the piecewise function:
\[
f(-4) = -4
\]
So, \( f(-4) = -4 \).

### Part 2: \( f(0) \)
Since \( 0 \) is equal to \( 0 \), we use the second part of the piecewise function:
\[
f(0) = 5(0) + 8 = 0 + 8 = 8
\]
So, \( f(0) = 8 \).

### Part 3: \( f(7) \)
Since \( 7 \) is greater than \( 0 \), we use the second part of the piecewise function:
\[
f(7) = 5(7) + 8 = 35 + 8 = 43
\]
So, \( f(7) = 43 \).

### Summary of Results:
- \( f(-4) = -4 \)
- \( f(0) = 8 \)
- \( f(7) = 43 \)

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would the function change if the condition for \( x = 0 \) were modified?
2. Can you determine the value of \( f(2) \) for the given function?
3. What is the domain of the given piecewise function?
4. How would the function behave if the condition were \( x \leq 0 \) instead of \( x < 0 \)?
5. What would be the value of \( f(-1) \)?

**Tip:** Understanding piecewise functions is key to analyzing how different conditions affect the output based on the input values.

Learn how to evaluate the piecewise function f(x) = { x if x < 0, 5x + 8 if x >= 0 } at specific values such as f(-4), f(0), and f(7). This problem covers the concept of piecewise functions and how to apply different conditions to compute function values. Suitable for high school students.

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