Algebra-1

According to the provided graph, we can see that the piecewise function consists of three parts:
a line segment for x < 1,
a horizontal line segment for 1 ≤ x < 4,
a line segment for x ≥ 4.


For the portion of the line where x < 1, we can see that it passes through the points (0, 1) and (1, -1).

To determine the equation, we can use the slope-intercept form of a linear equation, which is y = mx + b.
Plugging in the values from the first point, (0, 1), we get:

1 = m * 0 + b
1 = b

Substituting b = 1 into the equation, we have:

y = m * x + 1

Next, we can use the second point, (1, -1), to solve for the slope, m:

-1 = m * 1 + 1
-1 = m + 1
m = -2

Therefore, the equation for the portion of the line where x < 1 is:

f(x) = -2x + 1

For the portion of the line where 1 ≤ x < 4, we can see that it passes through the points (1 1), (2, 2) and (3, 3). By observing the graph, we can see that this portion of the line is ...