can anyone help me with this piecewise graph?

Question

anonymous · Answer

attachment

amistre64 · Answer

what about it?

amistre64 · Answer

we can make switches so that we can actually graph this as one function :)

anonymous · Answer

I need to find the equation to it. I haven't seen ones like this and I am really confused by it.

anonymous · Answer

it is multiple choice would you like me to list them?

amistre64 · Answer

well, you have 3 functions, each defined for a particular domain interval ....

what are the intervals of our domain?

amistre64 · Answer

well, they will be nice to guide us sure

anonymous · Answer

okay give me a moment I will draw them out.

amistre64 · Answer

in the meantime ... http://www.wolframalpha.com/input/?i=y%3D%283x%29%281-%28x%2B2%29%2F%7Cx%2B2%7C%29%2F2+%2B+%28%28x-8%29%2F2%2B4%29%28+%28x-5%29%2F%7Cx-5%7C+%2B+1%29%2F2+%2Bx%5E2%28-%28x%2B2%29%28x-5%29%2F%7C%28x%2B2%29%28x-5%29%7C+%2B1%29%2F2

anonymous · Answer

quick question. Will there always be 3 functions or can there be 2

amistre64 · Answer

you need to define the functions for the given intervals;  and then define a rule that for a given interval we graph a given function ... we piece it toghether.

it depends on the shape of the function,  in this case we have 3 difference functions and so we need to define 3 different intervals, one for each function

amistre64 · Answer

on the wolf, i just defined a switch that turns on and off at a given x value, that way i can turn a function on and off in a given interval

anonymous · Answer

okay so because 2 out of the 4 choices only have 2 functions so I can eliminate them.

amistre64 · Answer

notice the open points and the closed points

our intervals split up into:

-inf < x < -2  (open circle)

-2 <= x <= 5 (closed circle to closed circle)

5 < x < inf (open circle)

amistre64 · Answer

maybe, what are the options?

anonymous · Answer

here are the 4 possible answers

amistre64 · Answer

yeah, 3 functions, and th options make it clear that its the intervals that define the correct one

what would you say the intervals are?

amistre64 · Answer

is the first function stopping at x=-2?  or is it open at x=-2?

anonymous · Answer

it is open

amistre64 · Answer

then we never equal x=-2 .... therefore it is not defined at x=-2

what does this mean?  x <= -2?  or x < -2 ??

anonymous · Answer

x<-2 ?

amistre64 · Answer

correct, so we have our option we need to choose now

amistre64 · Answer

3 functions,  the first one is defined for x < -2

anonymous · Answer

oh! so that would be our answer?