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

Algebra ->  Linear-equations -> 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      Log On


   

Question 945386: our teacher has asked us to draw a detailed graph of the function:
+zf%28x%29+=+x%28x-1%29%2F%28x%2B1%29%28x-2%29+
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) About Me  (Show Source):
You can put this solution on YOUR website!
our teacher has asked us to draw a detailed graph of the function:
f%28x%29+=+x%28x-1%29%2F%28x%2B1%29%28x-2%29
***
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:
+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+%28x%5E2-x%29%2F%28x%5E2-x-2%29%29+
There is a lot more to explain about graphing rational expressions.
I hope this little bit of basics helps.