Question

Which statement is true about the discontinuities of the function f(x)? f (x) = StartFraction x 1 Over 6 x squared minus 7 x minus 3 EndFraction.

Answer 1

An asymptote is a straight line that approaches a curve indefinitely but does not intersect at any point. There are asymptotes at t $\dfrac{3}{2}\rm\ and\ \dfrac{-1}{3}$.

What is an asymptote?

An asymptote is a straight line that approaches a curve indefinitely but does not intersect at any point. In other words, when a curve approaches infinity, it approaches an asymptote line.

The function that is given to us is:

$f(x)=\dfrac{x+1}{6x^2-7x-3}$

As in the function, there is a fraction therefore, the denominator should not be zero in order for the function to be defined. Therefore, there are asymptotes at

$6x^2-7x-3 = 0$

Substituting the value in the formula of the quadratic equation we will get,

$D=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\D = \dfrac{-(-7)\pm\sqrt{(-7)^2-4(6)(-3)}}{2(6)}\\\\D =\dfrac{-(-7)\pm\sqrt{11}}{12} = \dfrac{3}{2}, \dfrac{-1}{3}$

Thus, there are asymptotes at  $\dfrac{3}{2}\rm\ and\ \dfrac{-1}{3}$.

Learn more about Asymptotes:

brainly.com/question/8493280