Linier graphic fuction f(x)=-3x+2 and domain = (-2,-1,0,1,2,3)

The linear function given is \( f(x) = -3x + 2 \). You want to determine the values of the function for the specified domain \( (-2, -1, 0, 1, 2, 3) \).

Let's compute \( f(x) \) for each value in the domain:

1. For \( x = -2 \):
   \[
   f(-2) = -3(-2) + 2 = 6 + 2 = 8
   \]
   
2. For \( x = -1 \):
   \[
   f(-1) = -3(-1) + 2 = 3 + 2 = 5
   \]
   
3. For \( x = 0 \):
   \[
   f(0) = -3(0) + 2 = 0 + 2 = 2
   \]
   
4. For \( x = 1 \):
   \[
   f(1) = -3(1) + 2 = -3 + 2 = -1
   \]
   
5. For \( x = 2 \):
   \[
   f(2) = -3(2) + 2 = -6 + 2 = -4
   \]
   
6. For \( x = 3 \):
   \[
   f(3) = -3(3) + 2 = -9 + 2 = -7
   \]

Thus, the corresponding values of the function for each point in the domain are:

\[
\begin{aligned}
f(-2) &= 8, \\
f(-1) &= 5, \\
f(0) &= 2, \\
f(1) &= -1, \\
f(2) &= -4, \\
f(3) &= -7.
\end{aligned}
\]

### Table of values:

| \( x \)   | \( f(x) \) |
|-----------|------------|
| -2        | 8          |
| -1        | 5          |
| 0         | 2          |
| 1         | -1         |
| 2         | -4         |
| 3         | -7         |

Would you like a more detailed explanation or any additional help?

Here are 5 related questions to expand on this:

1. How would the graph of this linear function look based on the table of values?
2. What is the slope of the line represented by \( f(x) = -3x + 2 \)?
3. Can you determine the \( y \)-intercept from the function's equation?
4. How would the function change if the slope were different, say \( f(x) = 2x + 2 \)?
5. What is the domain and range of this function?

**Tip:** To graph a linear function, use the slope-intercept form \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept.

Linier graphic function f(x)=-3x+2 and domain = (-2,-1,0,1,2,3)

Explore the linear function f(x) = -3x + 2 with domain (-2, -1, 0, 1, 2, 3). This problem includes a step-by-step solution, showing how to compute function values, understand slope, and interpret the graph. Suitable for Grades 6-8.

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