Question

Consider the given function.

ƒ(1): =
5,
I < -2
3, -2 <=<0
0,
0 <=<2
> 2
-3,
Which graph represents the given function?

Answer 1

Since the function is defined piecewise, we need to plot the points for each interval and connect them to form the graph.

For x < -2, f(x) = 5, which means that the graph is a horizontal line at y = 5 to the left of x = -2.

For -2 ≤ x ≤ 0, f(x) = 3, which means that the graph is a horizontal line at y = 3 between x = -2 and x = 0.

For 0 < x ≤ 2, f(x) = 0, which means that the graph is a horizontal line at y = 0 between x = 0 and x = 2.

For x > 2, f(x) = -3, which means that the graph is a horizontal line at y = -3 to the right of x = 2.

Therefore, the graph that represents the given function is:

```
|
5 | ________
| |
| __|
| |
| __|
3 |___________|
|
| __
| |
| __|
| |
0 |______|
|
| __
| __|
| |
|__|
-3 |
|
|
|
|
|
-2 0 2
```

Note: The graph consists of horizontal line segments at y = 5, y = 3, y = 0, and y = -3 for different intervals of x.