Question

What are the discontinuities of the function f(x) = the quantity x squared minus 16 over the quantity 4x plus 24

Answer 1

x^2 - 16
--------
4x + 24


when x = -6 the denominator 4x+24 = 0 so there is a discontinuity at x = -6

This is a vertical asymptote x = -6

There is also a sloping asymptote - you find this by getting the quotient
which is y = 0.25x - 1.5 This is the equation of this asymptote.

Answer 2

x= -6 is the point of discontinuity.

Explanation:

We have been given the expression

`(x^2-16)/(4x+24)`

The first thing to find the discontinuity is to factorize the given rational function:

After factorization we get:

We will use
`a^2-b^2=(a+b)(a-b)`

`here, a=x\text{and}b=4` we will get:

`(x+4)(x-4)=x^2-4^2`

we will get:

`((x+4)(x-4))/(4(x+6))`

Discontinuity is the point where value of the function becomes not defined

Here, the point of discontinuity is -6 because when denominator becomes zero. function becomes not defined.

It has vertical asymptote but function is not defined.

Hence it is the point of discontinuity.