Final answer:
The graph that represents the given piecewise-defined function is the plot on the left which shows a line from (0,2) to (3,8) and then a line from (3,8) to (7,4).
Step-by-step explanation:
The piecewise-defined function is as follows:
f(x) = x, x <-2
f(x) = -2, -2 ≤ x ≤ 1
f(x) = x-3, x > 1
To graph the function, we need to plot the points at the different intervals and connect them with straight lines. Here's how it looks:
- For x < -2, plot the points (x, x)
- For -2 ≤ x ≤ 1, plot the points (x, -2)
- For x > 1, plot the points (x, x-3)
Based on the given options, the graph that represents this piecewise-defined function is the plot on the left which shows a line from (0,2) to (3,8) and then a line from (3,8) to (7,4).