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
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-> 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
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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)
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.
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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
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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.
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d) Plot sufficient solution points
e) Sketch the graph of f(x)
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Cheers,
Stan H.
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