Evaluate the piecewise function at the given values of the independent variable.

f left parenthesis x right parenthesis equals left brace Start 2 By 2 Matrix 1st Row 1st Column 5 x plus 5 2nd Column if x less than 0 2nd Row 1st Column 3 x plus 7 2nd Column if x greater than or equals 0 EndMatrixf(x)=

5x+5

if x<0

3x+7

if x≥0

​(a) f left parenthesis negative 3 right parenthesisf(−3)

​(b) f left parenthesis 0 right parenthesisf(0)

​(c) f left parenthesis 3 right parenthesisf(3)

Question content area bottom

Part 1

​(a)

f left parenthesis negative 3 right parenthesisf(−3)equals=enter your response here

Part 2

​(b)

f left parenthesis 0 right parenthesisf(0)equals=enter your response here

Part 3

​(c)

f left parenthesis 3 right parenthesisf(3)equals=enter your response here

We are given a piecewise function:

\[
f(x) = \begin{cases} 
5x + 5 & \text{if } x < 0 \\
3x + 7 & \text{if } x \geq 0 
\end{cases}
\]

Now, let's evaluate the function at each of the given values.

### Part 1: \( f(-3) \)

Since \( -3 < 0 \), we will use the first part of the piecewise function:

\[
f(-3) = 5(-3) + 5 = -15 + 5 = -10
\]

Thus, \( f(-3) = -10 \).

### Part 2: \( f(0) \)

Since \( 0 \geq 0 \), we will use the second part of the piecewise function:

\[
f(0) = 3(0) + 7 = 0 + 7 = 7
\]

Thus, \( f(0) = 7 \).

### Part 3: \( f(3) \)

Since \( 3 \geq 0 \), we will again use the second part of the piecewise function:

\[
f(3) = 3(3) + 7 = 9 + 7 = 16
\]

Thus, \( f(3) = 16 \).

### Final answers:

(a) \( f(-3) = -10 \)

(b) \( f(0) = 7 \)

(c) \( f(3) = 16 \)

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Do you need more details or have any questions?

Here are five follow-up questions:

1. What is the general definition of a piecewise function?
2. How do you determine which part of the piecewise function to use?
3. How would the function change if the condition for \( x \geq 0 \) was modified to \( x > 0 \)?
4. What would \( f(1) \) be in this piecewise function?
5. Can you graph this piecewise function and identify any points of discontinuity?

**Tip:** Always check the conditions carefully to decide which piece of the function applies when working with piecewise functions!

Evaluate the piecewise function at the given values of the independent variable.

f(x) = { 5x + 5, if x < 0; 3x + 7, if x ≥ 0 }

(a) f(-3)
(b) f(0)
(c) f(3)

Learn how to evaluate a piecewise function with the example f(x) = { 5x + 5 if x < 0; 3x + 7 if x ≥ 0 }. Follow the step-by-step solution for calculating f(-3), f(0), and f(3), covering key concepts in algebra and function evaluation. Suitable for students in Grades 8-10.

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