Question

Can someone please explain how to figure out points of discontinuity? My book isnt doing me any good and i tried to look it up because its on my quiz but couldnt find any useful videos. Here's the question:

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

Answer 1

hi!!

Answer 2

set the denominator equal to zero and solve for \(x\) because you cannot divide by zero

Answer 3

same question as "what is the domain of the expression"

Answer 4

so how would i work that?
x+9=0 and x+7=0?

Answer 5

@misty1212

Answer 6

from here, you solve x+9=0 for x to get ???

that's one x value that will make the denominator zero

Answer 7

to get the other x value, you solve x+7=0 for x

Answer 8

ok. so x=-9 and x=-7?

Answer 9

correct, those two x values will make the entire denominator zero

Answer 10

since you cannot divide by zero, they are the values that must be excluded from the domain (there are discontinuities here)

Answer 11

ok.. does this make those two numbers points of discontinuity or is there more work to be done?

Answer 12

there are no other points of discontinuity because you can plug in any other x value (other than x = -9 or x = -7) and you wouldn't have a division by zero error

Answer 13

ah ok. thank you very much :)

Answer 14

you're welcome