Question

Graph the following piecewise function. State the values for f(0) and f(-2). Please show all of your work
f(x)={5-x^2 if x<_-3
{1 if -2<_x<_0
{x+6 if x>0

Answer 1

f(0) = 1
f(-2) = 1

Answer 2

can you show me how you got that please?

Answer 3

its defined in the domain:
for -2<x<0 , f(x) = 1

Answer 4

how do you graph it?

Answer 5

You graph it in pieces.
For x <= -3, you do just the part of the inverted parabola from -infinity up until x = -3, with a solid dot on the end at x = -3 to show that the -3 IS included.
Then a horizontal line for y=1, just between -2 & 0, again with solid dots. There will be a gap in your graph between x = -3 & x = -2.
The you do the line y = x+6, for x > 0.
I don't have time to graph it now, so if those last two pieces DON'T join, you need an open circle on the end at x = 0 to show that the zero is NOT included.

Answer 6

OH - at x = 0, x+6 = 6, but y=1 for the just before that, so the horizontal bit will NOT join the sloping line.