Question

Find any points of discontinuity for the rational function.. y= (x+6)(x+2)(x+8)/(x+9)(x+7)

Answer 1

-9 and -7. it is option c.

Explanation:

x=-9 x=-7

Answer 2

Setting the denominator to zero can help find the points of discontinuity for the rational function.

The denominator is (x+9)(x+7). Equating each factor to zero, the results are:
x+9 = 0; x=-9
x+7 = 0; x=-7

Substituting each of the values of x to the equation makes y undefined.

Finding also the oblique asymptotes if needed, one uses the long division process:


`x - 6`

`x^(2) + 16x + 63 \sqrt{ x^(3) + 10x^(2) + 16x +96 }`

`-({ x^(3) + 16x^(2) + 63x} )`

`-6x^(2) - 47x +96`

`-(6x^(2) -96x -378)`

`49x+474`

The oblique asymptote equation is : y=x-6