Limits Involving Infinity

Question

Which of the following is false for .

Options:

1. The y-axis is not an asymptote of f(x).
2. The x-axis is an asymptote of f(x).
3. x = -1 is not an asymptote of f(x).
4. x = 1 is an asymptote of f(x).

Answer 1

The easiest way to answer this question is to plot the function.

Once you do you will see that #3 is false.

To do it analytically write the fraction as 5(x²-x-1)/(x⁴-1) for x not equal to 0.