Given a piecewise function:
To graph the function follow the steps below:
<h3>Step 1</h3>
Graph the first function, f(x) = 3x - 5
Plot two points with x- coordinates - 1 and 0. We considered x ≤ -1 when selecting points.
- f(-1) = 3(-1) - 5 = - 8
- f(-2) = 3(-2) - 5 = - 11
Make point (- 1, - 8) a full dot and connect two points, then extend the line to the left from x = -2.
<h3>Step 2</h3>
Graph the second function, f(x) = - 2x + 3.
Plot both endpoints with x - coordinates of - 1 and 4.
- f(-1) = - 2(-1) + 3 = 5
- f(4) = - 2(4) + 3 = - 5
Make both points (-1, 5) and (4, 5) open dots and connect together.
<h3>Step 3</h3>
Graph the third function, f(x) = 2.
Every point of this function has the value of 2, we are interested in the endpoint when x = 4.
Make this point a full dot and make a line parallel to the x-axis, to the right from the plotted point.
Now we have the full graph, <u>see attached</u>.