SOLUTION: F(x)= (x-1)/(x�-4) Find the domain of f(x). Describe the horizontal and vertical asymptotes and any symmetry of the graph of f(x). Find the x and y intercepts.

Question 435117: F(x)= (x-1)/(x�-4)
Find the domain of f(x).
Describe the horizontal and vertical asymptotes and any symmetry of the graph of f(x).
Find the x and y intercepts.

Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Factoring the denominator gives us:

The domain is the set of all x-values for which the function is defined.
The function is undefined for values of x which make the denominator equal to zero.
The function is undefined at x = -2, 2.
So the domain of f(x) is (-,-2) U (-2,2) U (2,)
The vertical asymptotes are x = -2 and x = 2.
The horizontal asymptote is y = 0, since for large positive and negative values of x,
the function approaches but never reaches zero.
The x-intercept is the value of the function when y=0. So the x-intercept is x=1.
The y-intercept is obtained by evaluating the function at x=0
f(0) = -1/-4 = 1/4
So the y-intercept is y= 1/4

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