SOLUTION: f(x)= x^2-4x+4/x-1 a) Identify the x & y-intercepts b) Find all vertical, horizontal and slant asymptotes c) Check for symmetry d) Plot sufficient solution points e) Sketc

Question 585599: f(x)= x^2-4x+4/x-1
a) Identify the x & y-intercepts
b) Find all vertical, horizontal and slant asymptotes
c) Check for symmetry
d) Plot sufficient solution points
e) Sketch the graph of f(x)

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
f(x)= (x^2-4x+4)/(x-1)
a) Identify the x & y-intercepts
x-intercept ?
Let y = 0; then x^2-4x+4 = (x-2)^2 = 0
x = 2 is the x-intercept.
----
y-intercept ?
Let x = 0, then y = 4/(-1) = -4
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b) Find all vertical, horizontal and slant asymptotes
Vertical with x = 1
Horizontal with y = x^2/0x^2 is undefined.
So no horizontal asymptote.
Slant: (x^2-4x+4)/(x-1) = (x-3)(x-1)+1
Slant asymptote: y = x-3
-----------------------------------
c) Check for symmetry
f(-x) = (x^2+4x+4)/(-x-1)
-f(-x) = (x^2+4x+4)/(x+1)
Since f(x) is not equal to f(-x), no y-axis symmetry.
Since f(x) is not equal to -f(-x), no origin symmetry.
-------------------------------------
d) Plot sufficient solution points
e) Sketch the graph of f(x)

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Cheers,
Stan H.

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