Question

Consider the following equation: f (x) = startfraction x squared 4 over 4 x squared minus 4 x minus 8 endfraction. name the vertical asymptote(s). ✔ x = -1 and x = 2 because m < n m = n am < bn am = bn this is where the function is undefined

Answer 1

The vertical asymptotes of the function f(x) are at x = -1 and x = 2, which are found by setting the denominator of the function equal to zero and solving the resultant quadratic equation.

Step-by-step explanation:

The question pertains to identifying the vertical asymptotes of the function f(x) = \(\frac{x^2}{4x^2 - 4x - 8}\). Vertical asymptotes occur where the function is undefined, which corresponds to the values of x where the denominator is equal to zero. To find these values, we set the denominator to zero and solve for x:

\(4x^2 - 4x - 8 = 0\)

To solve this quadratic equation, we can either factor it (if it is factorable), or use the quadratic formula. It turns out that the quadratic can be factored as:

\((2x+2)(2x-4) = 0\)

Thus, the solutions are \(x = -1\) and \(x = 2\). These are the vertical asymptotes of the function since the function will not be defined at these points.