The piecewise function represented by the graph is
f(x) = 3/2x - 1 , for 0 ≤ x ≤ 2.
x = 2
f(x) = -2x + 5 , for 2 < x < 3.
f(x) = -1, for x > 3
Writing a piecewise function represented by the graph.
From the question, we have the following parameters that can be used in our computation:
The graph
The first linear piece goes through the points (0, -1) and (2, 2).
This can be represented by the equation of a line:
f(x) = mx - 1, where m is the slope.
Using the other point, we have
2m - 1 = 2
m = 3/2
So,
f(x) = 3/2x - 1 , for 0 ≤ x ≤ 2.
The second linear piece begins at an open dot at (2, 2) and ends at a closed dot at (2, 1).
This is a vertical line
So,
x = 2
The third linear piece goes through the points (2, 1) and (3, -1).
This can be represented by the equation of a line:
2m + c = 1
3m + c = -1
So, we have
m = -2
c = 1 - 2 * -2
c = 5
So,
f(x) = -2x + 5 , for 2 < x < 3.
Hence, the function is
f(x) = 3/2x - 1 , for 0 ≤ x ≤ 2.
x = 2
f(x) = -2x + 5 , for 2 < x < 3.
f(x) = -1, for x > 3