For the indicated​ function, find the values 

​f(negative 4−4​), 

​f(00​), 

and 

​f(66​).

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 EndMatrixf(x)=

       x, if x<0

5x+8, if x≥0

Question content area bottom

Part 1

​f(negative 4−4​)equals=enter your response here

Part 2

​f(00​)equals=enter your response here

Part 3

​f(66​)equals=enter your response here

Given the piecewise function:

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

We need to find the values of \( f(-4) \), \( f(0) \), and \( f(6) \).

### Part 1: Calculate \( f(-4) \)
Since \(-4 < 0\), we use the first part of the function:

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

### Part 2: Calculate \( f(0) \)
Since \(0 \geq 0\), we use the second part of the function:

\[
f(0) = 5(0) + 8 = 0 + 8 = 8
\]

### Part 3: Calculate \( f(6) \)
Since \(6 \geq 0\), we use the second part of the function:

\[
f(6) = 5(6) + 8 = 30 + 8 = 38
\]

### Final Answers
\[
f(-4) = -4
\]
\[
f(0) = 8
\]
\[
f(6) = 38
\]

Would you like further details or have any questions?

### Relative Questions:
1. How do you graph a piecewise function like the one given?
2. What are the key steps to evaluating a piecewise function at a given value?
3. How do you determine where a piecewise function is continuous?
4. How would you define a piecewise function with more than two pieces?
5. What are the applications of piecewise functions in real-world scenarios?

### Tip:
Always carefully check the conditions in a piecewise function before substituting values to ensure you're using the correct piece of the function.

Learn how to evaluate values of a piecewise function f(x) = { x, if x < 0; 5x + 8, if x ≥ 0 }. Find the specific values for f(-4), f(0), and f(6) using the correct piece of the function. Suitable for high school students and anyone interested in piecewise functions.

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