SOLUTION: F(x)= (x-1)/(x²-4) 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.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: F(x)= (x-1)/(x²-4) 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.       Log On


   

Question 435117: F(x)= (x-1)/(x²-4)
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) About Me  (Show Source):
You can put this solution on YOUR website!
Factoring the denominator gives us:
f%28x%29=%28x-1%29%2F%28x%2B2%29%28x-2%29
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 (-infinity,-2) U (-2,2) U (2,infinity)
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
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%28x-1%29%2F%28%28x%2B2%29%28x-2%29%29%29