Respuesta :
x^2 - 16
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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.
--------
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:
x= -6 is the point of discontinuity.
Step-by-step explanation:
We have been given the expression
[tex]\frac{x^2-16}{4x+24}[/tex]
The first thing to find the discontinuity is to factorize the given rational function:
After factorization we get:
We will use [tex]a^2-b^2=(a+b)(a-b)[/tex]
[tex]here, a=x\text{and}b=4[/tex] we will get:
[tex](x+4)(x-4)=x^2-4^2[/tex]
we will get:
[tex]\frac{(x+4)(x-4)}{4(x+6)}[/tex]
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.
