Question

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

Answer 1

Answer:

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

Step-by-step explanation:

The rational function is given as:

$y=\frac{4x^2+1}{x^2-1}$

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

$x^2-1=0\\x^2=1\\x=\pm \sqrt{1}\\ x= -1\ and\ x = 1$

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