Given the function:
 
𝑓
(
𝑥
)
=
{
3
𝑥
+
7
𝑥
<
0
3
𝑥
+
14
𝑥
≥
0


Calculate the following values:
𝑓
(
-
1
)
=
   
𝑓
(
0
)
=
   
𝑓
(
2
)
=
   

The given piecewise function is:

\[
f(x) =
\begin{cases}
3x + 7, & \text{if } x < 0 \\
3x + 14, & \text{if } x \geq 0
\end{cases}
\]

Now, let's evaluate \( f(-1) \), \( f(0) \), and \( f(2) \) based on the given function:

### 1. \( f(-1) \) (since \( -1 < 0 \), use \( 3x + 7 \)):
\[
f(-1) = 3(-1) + 7 = -3 + 7 = 4
\]

### 2. \( f(0) \) (since \( 0 \geq 0 \), use \( 3x + 14 \)):
\[
f(0) = 3(0) + 14 = 0 + 14 = 14
\]

### 3. \( f(2) \) (since \( 2 \geq 0 \), use \( 3x + 14 \)):
\[
f(2) = 3(2) + 14 = 6 + 14 = 20
\]

### Final results:
\[
f(-1) = 4, \quad f(0) = 14, \quad f(2) = 20
\]

Would you like more details or clarifications on any of these steps?

Here are 5 related questions to expand your understanding:
1. How do you define piecewise functions in general?
2. What would \( f(3) \) be for this function?
3. How do you graph a piecewise function like this one?
4. What is the domain of the function \( f(x) \)?
5. Can you determine if the function is continuous at \( x = 0 \)?

**Tip:** Always check the domain of each piece in a piecewise function before applying the function rules.

Given the function:

f(x) =
{
3x + 7, x < 0
3x + 14, x ≥ 0
}

Calculate the following values:
f(-1) = 
f(0) = 
f(2) = 

Learn how to evaluate a piecewise linear function at specific points. This example problem demonstrates the process of calculating f(-1), f(0), and f(2) for a function defined by different linear equations based on the value of x. Suitable for students in Grades 9-11.

Math Problem Statement

𝑓 ( 𝑥 )

Calculate the following values: 𝑓 (

1 )

𝑓 ( 0 )

𝑓 ( 2 )

Solution

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