Graph the function

Question

F(x) = |x+4| -1 if x < -2

          -x²+3 if -2<x<3

           X if x>3

Answer 1

Well, I'm not sure how to show you on here how to graph, but pick some x-values.

 

f(-5) = |-5 + 4| - 1 = 1 - 1 = 0

 

(-5,0)

 

f(-4) = |-4 + 4| - 1 = 0 - 1 = -1

 

(-4,-1)

 

f(-3) = |-3 + 4| - 1 = 1 - 1 = 0

 

(-3,0)

 

f(-2) = |-2 + 4| - 1 = 2 - 1 = 1

 

(-2,1)

 

Because we don't have "or equal to" there is a circle on (-2,1).

 

f(-2) = -(-2)² + 3 = -4 + 3 = -1

 

(-2,-1)

 

Again, because of no "or equal to" we have a circle at (-2,-1).

 

f(-1) = -(-1)² + 3 = -1 + 3 = 2

 

(-1,2)

 

Etc etc until...

 

f(3) = -(3)² + 3 = -9 + 3 = -6

 

We have a circle at (3,-6).

 

(3,3) with an open circle. (4,4), (5,5), etc.

 

Got it?