I need hep to find the vertical and horizental asymptotes.

Question

f(x) = x − 3/x + 3
f(x)=x^2/x^2-9
f(x)=1-x^2/x^2-2x+1
f(x)=x^2-4/x^4-16
f(x)=x(x-1)(x-2)/x^4-x^2
f(x)=e^x
f(x) = ln x

Answer 1

vertical asymptotes are where the denominator is zero and the numerator is not zero -- in the reduced fraction.
So factor the top and bottom and cancel any common factors.

horizontal asymptotes are
y=0 if the degree of the numerator is less than that of the denominator.
y = k where k is the quotient of the coefficients (top/bottom) of the highest power of x

e^x and lnx are special cases, since they are not rational functions.
Look 'em up.

Answer 2

Use Internet help.

In google type:

asymptotes calculator emathelp

When you see list of results click on:

Asymptote Calculator-emathelp

When page be open in rectangle paste your function and click option Calculate.

You will see result step by step.

Don’t forget to write parentheses in your equations, so write:

(x-3)/(x+3)

x^2/(x^2-9)

(1-x^2)/(x^2-2x+1)

(x^2-4)/(x^4-16)

x(x-1)(x-2)/(x^4-x^2)

You will have to factor some of these expressions.

In google type:

Factoring calculator emathhelp

When you see list of results click on:

Factoring Calculator-emathhelp

paste:

(1-x^2)/(x^2-2x+1)

and click option CALCULATE

then paste:

(x^2-4)/(x^4-16)

and click option CALCULATE

then paste:

x(x-1)(x-2)/(x^4-x^2)

and click option CALCULATE

You will see result step by step