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MrRissso [65]
3 years ago
13

Find any points of discontinuity for the rational function. y=x-5/x^2-7x-8

Mathematics
2 answers:
Crazy boy [7]3 years ago
4 0

Answer:

<em>The function is not continuous at </em><em>x= -1</em><em> and </em><em>x= 8</em>

Step-by-step explanation:

The given function is,

y=\dfrac{x-5}{x^2-7x-8}

Factoring the denominator,

=x^2-7x-8

=x^2-8x+x-8

=x(x-8)+1(x-8)

=(x+1)(x-8)

Now the function becomes,

y=\dfrac{x-5}{(x+1)(x-8)}

The function is not defined (it does not exist) for x= -1 and for x= 8, because the denominator is zero for those values of x.

To be continuous, the function has to be defined. So at those points the function is not continuous.

*At x= -1 and at x= 8 , the function has a vertical asymptote.

kotegsom [21]3 years ago
3 0
For discontinuity of the function:
x² - 7 x - 8 ≠ 0
x² - 8 x + x - 8 = 0
x ( x - 8 ) + ( x - 8 ) ≠ 0
( x - 8 ) ( x + 1 ) ≠ 0
The points of discontinuity are: x = - 1 and x = 8.
As for the Domain of the function:
x ∈ ( - ∞, - 1 ) ∪ ( - 1 , 8 ) ∪ ( 8, +∞ ). 
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