Answer:
See the attachment for the graph of the piecewise function.
Plot points (2, -2), (-4, -8) and (4, -6).
Draw a straight line from (2, -2) through (-4, -8).
Draw a straight line from (2, -2) through (4, -6).
Add arrows at the ends of the lines to show that they continue indefinitely in that direction.
Explanation:
Piecewise functions have multiple pieces of curves and/or lines, where each piece corresponds to its definition over an interval.
Given piecewise function:

Therefore, the function has two definitions:
- f(x) = x - 4 when x is less than 2.
- f(x) = -2x + 2 when x is more than or equal to 2.
When graphing piecewise functions:
- Use an open circle where the endpoint is not included in the interval.
- Use a closed circle where the endpoint is included in the interval.
- Use an arrow to show that the function continues indefinitely in that direction.
First piece of the function
Substitute the endpoint x = 2 into the first function:

As x = 2 is not included in the interval, place an open circle at point (2, -2).
To help graph the line, find another point on the line by inputting another value of x that is less than 2 into the same function:

Plot point (-4, -8) and draw a straight line from the open circle at (2, -2) through point (-4, -8). Add an arrow at the other endpoint to show it continues indefinitely as x → -∞.
Second piece of the function
Substitute the endpoint x = 2 into the second function:

Notice that the endpoint of this piece of the function when x = 2 is the same as the endpoint of the first piece of the function when x = 2.
Therefore, we need to remove the open circle we placed earlier as (2, -2), as the function is continuous at x = 2.
To help graph the line of the second piece of the function, find another point on the line by inputting another value of x that is more than 2 into the same function:

Plot point (4, -6) and draw a straight line from (2, -2) through point (4, -6). Add an arrow at the other endpoint to show it continues indefinitely as x → ∞.