Given a piecewise function:
[tex]f(x) = \left\{ \begin{array}{rcl} 3x-5} & \mbox{if} & x \leq-1 \\ -2x+3 & \mbox{if} & -1 < x < 4 \\ {2} & \mbox{if} &x \geq4 \end{array}\right.[/tex]
To graph the function follow the steps below:
Step 1
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.
Step 2
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.
Step 3
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, see attached.
