These piecewise functions are several graphs pieced together. Where one ends the other begins.
The greater than (> or <) symbol means an open circle at that point. If it is greater than or equal to (>=) then you put a closed solid circle.
start with the first one
-2x + 3 where -4 =< x < -1
put in these values for x
solid circle at (-4, 11)
open circle at (-1, 5)
graph is a straight line so connect the circles
next one
|2x -1| where -1 < x < 2
absolute value graphs are V-SHAPED where y is always positive. solve for vertex (x, 0)
0 = 2x -1
x = 1/2
(1/2, 0) vertex of V
solve for endpoints, both are open circles
(-1, 3)
(2, 3)
next one is easy. it's just a solid point
When y = 5 ; x = 2
(2,5)
last is a parabola, or just half of a parabola, aka bowl shaped graph
3x^2 - 1 when x > 2
plug in x = 2
open circle at (2, 11)
you can put in another x value greater than 2 to find a second point to help draw the graph but it's just a curve upward that continues with an arrow, no endpoint
