See graph below
Explanation:
f(x) = 3x - 5
for interval x ≤ -1
This means x is equal to -1 or less than - 1
values of x = -1, -2, -3,....
when x = -1
f(x) = 3(-1) - 5 = -8
when x = -2
f(x) = 3(-2) - 5 = -11
when x = -3
f(x) = 3(-3) - 5 = -14
f(x) = -2x + 3
for interval -1 < x < 4
Interval shows x is greater than -1 but less than 4
x = 0, 1, 2, 3
when x = 0
f(x) = -2(0) + 3 = 3
when x = 1
f(x) = -2(1) + 3 = 1
when x = 2
f(x) = -2(2) + 3 = -1
when x = 3
f(x) = -2(3) + 3 = -3
f(x) = 2 if the the interval is x ≥ 4
This means for x greater than or equal to 4, the function will be constant. we will have only 2
Sketching the graph of the piece wise function:
There is an equal sign attached to -1 in the first function, so the circle at x = -1 is shaded
The ends of the second function is open as there is no equal sign attached to the inequalities
There is an equal sign attached to 4 in the third function, so the circle at x = 4 is shaded
The arrows in function 1 and 3 indicate the line doesn't end
