could someone assist me, i cant seem to find any reference in my notes. not searching for answers, more of a guide on how to approach the question. produce the following graph for -2 3}}

Question

could someone assist me, i cant seem to find any reference in  my notes. not searching for answers, more of a guide on how to approach the question.

produce the following graph for -2<x<5

f(x)={{4 - x^2, x < 1}, {(3/2) x + 3/2, 1 <= x <= 3}, {x + 3, x > 3}}

dumbcow · Answer

ok for piecewise, you need to get your endpoints
f(-2) = 4-(-2)^2 = 0
f(1) = 4 - 1 = 3   (open)
f(1) = 3/2 + 3/2 = 3 (closed)
f(3) = 3/2(3) + 3/2 = 6 (closed)
f(3) = 3+3 = 6 (open)
f(5) = 5+3 = 8

plot these points, then connect them with appropriate shape
interval 1 --- parabola
interval 2,3  ---- line

dumbcow · Answer

lines are easy

for parabola, draw what the entire graph is , then look at shape in interval of [-2,1]
insert that shape into piecewise graph

anonymous · Answer

thank you @dumbcow. i shall let you know of the outcome

dumbcow · Answer

ok:)