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vampirchik [111]
2 years ago
9

Let f(x)= x(2x-3)/(x+2)x. Find the domain, vertical and horizontal asymptote

Mathematics
1 answer:
Reptile [31]2 years ago
7 0

Step-by-step explanation:

Domain of a rational function is everywhere except where we set vertical asymptotes. or removable discontinues

Here, we have

\frac{x(2x - 3)}{(x + 2)x}

First, notice we have x in both the numerator and denomiator so we have a removable discounties at x.

Since, we don't want x to be 0,

We have a removable discontinuity at x=0

Now, we have

\frac{2x - 3}{x + 2}

We don't want the denomiator be zero because we can't divide by zero.

so

x + 2 = 0

x =  - 2

So our domain is

All Real Numbers except-2 and 0.

The vertical asymptors is x=-2.

To find the horinzontal asymptote, notice how the numerator and denomator have the same degree. So this mean we will have a horinzontal asymptoe of

The leading coeffixent of the numerator/ the leading coefficent of the denomiator.

So that becomes

\frac{2}{1}  = 2

So we have a horinzontal asymptofe of 2

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