Show all work to identify the asymptotes and zero of the function f(x) = 3x/x^2-9

The vertical asymptotes are +3 and -3 and the horizontal asymptote is 0 and this can be determined by putting the denominator equal to zero.

Given :

Function  -    

The following steps can be used to determine the asymptotes and zero of the given function.

Step 1 - Determine the vertical asymptotes of the given function.

(x-3)(x+3) = 0

x = +3 , -3

Step 2 - Determine the horizontal asymptotes of the given function.

y = 0

The vertical asymptotes are +3 and -3 and the horizontal asymptote is 0.

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Step-by-step explanation:

Obviously, −3 and 3 would be set to equal , knowing that they are the roots of 9. Or, you can choose to factor. The divisor of is a product of two binomials:

Then, knowing that you set both factors equal to zero, −3 and 3 would be your zeros, which are also two non-removable discontinuities, or vertical asymptotes because you cannot have zero in the denominator.

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step-by-step explanation: