# graphing functions

• Jan 11th 2007, 01:29 PM
leviathanwave
graphing functions
Hey guys, I need some help on this graphing stuff. Any help is MUCH appreciated.

1. Sketch f(x) = { -x-3 if x < 0 }{lxl if 0 <or= x <2}{3 if x >or= 2}

If I'm not mistaken, doesn't the last piece get ignored since it goes against the first two?

2. f(x) = -(x+2)^3 +1
a. What type of function is it? <--- i don't really know what she's looking for... maybe a cubing function?
b. Sketch, showing all intermediate graphs. <---- again, unsure what ALL intermediate would mean...

3. g(x) = square root(4 - x) +2
a. Domain <--- this one i think i got, (-inf. , 4)U(4, inf.) right?
b. find the y-intercept <--- do you do this by setting x = 0?
c. Sketch, showing all intermediate graphs

Again, thanks a lot for ANY help at all. Kinda lengthy, sry....
• Jan 11th 2007, 07:25 PM
CaptainBlack
Quote:

Originally Posted by leviathanwave
Hey guys, I need some help on this graphing stuff. Any help is MUCH appreciated.

1. Sketch f(x) = { -x-3 if x < 0 }{lxl if 0 <or= x <2}{3 if x >or= 2}

If I'm not mistaken, doesn't the last piece get ignored since it goes against the first two?

The sketch should look something like that in the attachment (ignore the
vertical lines they are just an artifact of the plotting software)

RonL
• Jan 11th 2007, 07:32 PM
CaptainBlack
Quote:

Originally Posted by leviathanwave
2. f(x) = -(x+2)^3 +1
a. What type of function is it? <--- i don't really know what she's looking for... maybe a cubing function?
b. Sketch, showing all intermediate graphs. <---- again, unsure what ALL intermediate would mean...

a) its a cubic.

b) start with a sketch of y=-x^3, then sketch it translated horizontaly 2
units to the left to get a sketch of y=-(x+2)^3. Then sketch it translated
upwards by 1 unit to get a sketch of y-1=-(x+2)^3, or y=-(x+2)^3+1.

RonL
• Jan 11th 2007, 07:36 PM
CaptainBlack
Quote:

Originally Posted by leviathanwave
3. g(x) = square root(4 - x) +2
a. Domain <--- this one i think i got, (-inf. , 4)U(4, inf.) right?
b. find the y-intercept <--- do you do this by setting x = 0?
c. Sketch, showing all intermediate graphs

a) For this to be defined (as a real number) we need that (4-x)>=0, or
x<=4, as otherwise the square root does not exists. So the domain here is:

(-inf, 4]

b) Yes

RonL