What are the equations of the asymptotes of the graph of the function f(x)=3x^2-2x-1/x^2+3x-10

Vertical asymptotes

Horizontal asymptote

Step-by-step explanation:

We have the function and we want to find its asymptotes.

First we find their vertical asymptotes.

To do this we must factor the denominator of the expression.

We must look for two numbers that when adding them obtain 3, and when multiplying those same numbers, obtain -10.

The searched numbers are 5 and -2

Then the factors are:

Since the division between zero is not defined then when x tends to -5 the function tends to infinity and when x tends to 2 the function tends to infinity.

So the vertical asymptotes will be the straight lines:

The horizontal asymptote is calculated as:

The highest exponent of the function is 2. Then the terms with exponents less than 2 tend to zero

Then

Therefore the horizontal asymptote is:

Observe the attached image

8/k

step-by-step explanation: