Question

Find Vertical Asymptote(s) for y= (4x^2 +1) / (x^2 -1)

Answer 1

Vertical asymptotes are at
`x=-1\ and\ x=1`.

Explanation:

The rational function is given as:

`y=(4x^2+1)/(x^2-1)`

Vertical asymptotes are those values of
`x` for which the function is undefined or the graph moves towards infinity.

For a rational function, the vertical asymptotes can be determined by equating the denominator equal to zero and finding the values of
`x`.

Here, the denominator is
`x^2-1`

Setting the denominator equal to zero, we get

`x^2-1=0\\x^2=1\\x=\pm √(1)\\ x= -1\ and\ x = 1`

Therefore, the vertical asymptotes occur at
`x=-1\ and\ x=1`.