Domain of f (x) = (- x2 + 1) / (-3 x2 + 27)
The domain of the function is the set of input for which function is real and defined.
Take the denominator and compare to zero
Solve – 3 x2 + 27 = 0 given x = 3 and x = -3
The point x = 3 and x = -3 are undefined. Hence the domain of the function is x < - 3 0r -3 < x < 3 or x > 3.
For rational function, the vertical asymptotes are the undefined points, also known as the zeros of the denominator, of the simplifies function. The undefined points are x = 3 and x = -3.
Hence, the vertical asymptotes are x = 3 and x = -3.
If denominator’s degree > numerator’s degree, the horizontal asymptotes is the
X – axis: y = 0.
If the degree is equal, the asymptote is y = numerator’s leading coefficient / denominators leading coefficient.
Here in the function:
The degree of the denominator = 2. The degree of the numerator is 2.
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