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:

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.