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....

Quote:

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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

Quote:

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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...

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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

Quote:

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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

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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