Question

Where are the asymptotes for the following function located? f (x) = StartFraction 7 Over x squared minus 2 x minus 24 EndFraction.

Answer 1

The the asymptotes are at x = -4 and 6.

Now we have given

$f(x)=\frac{7}{x^2-2x-24}$

f(x) = ∞, is not defined for x²- 2x - 24 = 0.

.What is the regular hyperbola?

A rectangular parabola is a hyperbola having three transverse axes and the conjugate axis of equal length. The arcs of a rectangular hyperbola are the same as the arc of the circle. The general equation of the rectangular hyperbola is x² + y² = a²

Given  function is a,

$f(x)=\frac{7}{x^2-2x-24}$

To find the asymptotes of a hyperbola.

f(x) = ∞, is not defined when the denominator is 0

$x^{2} - 2x - 24 = 0\\x^{2} - (6-4) x - 24 = 0x^{2} -6x + 4x -24 = 0( x - 6 ) ( x + 4 ) = 0$

As the f(x) is not defined at -4 and 6.

Therefore,

The the asymptotes are at x = -4 and 6.