Answer:
Here's how to graph the piecewise function:
First, we graph the function for the first interval, which is f(x) = 3x - 5 when x ≤ -1. This is a straight line with a slope of 3 and a y-intercept of -5. Since this interval includes -1, we draw a closed circle at x = -1 to indicate that it is included in the interval. The line is decreasing as x increases.
Next, we graph the function for the second interval, which is f(x) = -2x + 3 when -1 < x < 4. This is also a straight line, but with a slope of -2 and a y-intercept of 3. Since this interval does not include -1, we draw an open circle at x = -1 to indicate that it is not included in the interval. We also draw an open circle at x = 4 to indicate that it is not included in the interval. The line is increasing as x increases.
Finally, we graph the function for the third interval, which is f(x) = 2 when x ≥ 4. This is a horizontal line at y = 2. Since this interval includes 4, we draw a closed circle at x = 4 to indicate that it is included in the interval.
When we put all three intervals together, we get a graph that looks like this:
```
| /
2 | /
| /
| /
| /
| /
| /
| /
| /
|/
_______|_____________
-1 4
```
The graph consists of a downward-sloping line from (-∞, -1], an upward-sloping line from (-1, 4), and a horizontal line from [4, ∞).