Question

Which statement is true about the discontinuities of the function f(x) x+1/6x^2-7x-3

Answer 1

Answer:

Option A.

Step-by-step explanation:

The given function is f(x) = $\frac{(x+1)}{6x^{2}-7x-3}$

Now we will factorize the denominator first.

6x² - 7x - 3 = 6x² - 9x + 2x - 3

                  = 3x(2x - 3) + 1(2x - 3)

                  = (3x + 1)(2x - 3)

If (3x + 1) = 0

x = $-\frac{1}{3}$

If (2x - 3) = 0

x = $\frac{3}{2}$

Since numerator and denominator has no common factor

So, $x=\frac{3}{2},-\frac{1}{3}$ the given function has the vertical asymptotes.

Option A. is the correct option.

Answer 2

We are given with the function f(x)= (x+1)/(6x^2-7x-3) where we are asked in the problem to determine the discontinuities of the functions. In this case, we must find the horizontal asymptotes that is to determine the roots of the function at the denominator. Asymptotes are functions in which they do not necessarily touch the axes, just approaching. Then,

6x^2-7x-3 = 0 
(x-3/2) * (x+1/3) = 0
x=3/2 and x=−1/3
The option applicable in this case is option B. there are holes at x= 3/2 and x=-1/3