# Find the domain and the vertical and horizontal asymptotes-2 1f(x)- 3x2 + 27DomainVertical asymptote(s): æ=Horizontal asymptote(s): y =

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2 views help_outlineImage TranscriptioncloseFind the domain and the vertical and horizontal asymptotes -2 1 f(x) - 3x2 + 27 Domain Vertical asymptote(s): æ = Horizontal asymptote(s): y = fullscreen
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Step 1

Part (a):

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.

Step 2

Part (B)

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.

Step 3

Part (c)

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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