SOLUTION: our teacher has asked us to draw a detailed graph of the function: {{{ zf(x) = x(x-1)/(x+1)(x-2) }}} i know roughly what the graph will look like but how to i give working to

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Question 945386: our teacher has asked us to draw a detailed graph of the function:

i know roughly what the graph will look like but how to i give working to show how i find asymptotes roots intercepts
any help and step would be appreciated,
thanks

Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
our teacher has asked us to draw a detailed graph of the function:

***
To find the vertical asymptotes, set the denominator=0, then solve for x.
(x+1)(x-2)=0
x+1=0
x≠-1
or
x-2=0
x≠2
vertical asymptotes are: x=-1 and x=2
..
Horizontal Asymptotes:
When the power of the numerator is equal to the power of the denominator(both 1 in this case) divide the lead coefficient of the numerator by the lead coefficient of the denominator=1/1=1. horizontal asymptote: y=1
..
x-intercepts:
set y=0, then solve for x
x(x-1)=0
x=0, x=1 are the x intercepts
..
another aid you can use to check your graph is the number line which show what the sign should be in the intervals between the critical points.
<..+..-1..-..0..+..1..-..2..+..>
see the graph below:

There is a lot more to explain about graphing rational expressions.
I hope this little bit of basics helps.

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