Question
Asked Oct 17, 2019
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Find the domain and the vertical and horizontal asymptotes
-2 1
f(x)
- 3x2 + 27
Domain
Vertical asymptote(s): æ
=
Horizontal asymptote(s): y =
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Find the domain and the vertical and horizontal asymptotes -2 1 f(x) - 3x2 + 27 Domain Vertical asymptote(s): æ = Horizontal asymptote(s): y =

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Expert Answer

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.

&n...

numerator's leading coefficient
denominator's leading coefficient
y =
3
1
y =
3
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numerator's leading coefficient denominator's leading coefficient y = 3 1 y = 3

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