Need help ASAP with piecewise function?

Question

Graph the piecewise function

f(X) = { -x^2, -2 < or equal to x < 1

-2, x=1

3x+5, 1 < x < or equal to 3

how do i do it?

Answer 1

Hi,

to graph this the easiest way would be to consider it as if it were 3 different functions f(X) = -x^2, f(X) = -2 and f(X) = 3x+5.

For the first one plug in -2 which would give -4 and then plug in -1 which gives -1 and also put 0 which gives 0. you can also put -0.5 and 0.5 which gives 0.25 and finaly 1 which gives -1.

hence you draw a line that joins f(-2)=-4, f(-1)=-1, f(-0.5)=-0.25, f(0)=0, f(0.5)=-0.25 and f(1)=-1

f(1)=-1 (is not really this but this part of the function really stops at f(0.99999999...)=-0.999999999

the next step would be to put a dot at f(1)=-2

Finaly plug in a few numbers from 1 to 3 in f(x)=3x+5 and join the points and there you go you have the piecewise function.