Question

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

Answer 1

Here We've
\[y=\frac{(x+6)(x+2)(x+8)}{(x+9)(x+7)}
\]
@Math4Life What is a discontinuity ? What do you think y is when x=-8?

Answer 2

I just solved and got the answer as x = –6, x = –2, x = –8

Answer 3

Oh these won't be discontinuities, y is zero which is finite. Zeros doesn't count as discontinuities. Find values of x which makes difficult to evaluate y or y cease to exist

Answer 4

@ash2326 u rigth!

Answer 5

@ash2326 I solved and got x = –6, x = –2, x = –8 am I correct or no?

Answer 6

No x=-6 y=0 which is finite, we didn't have any difficulty in evaluating this and so for x=-2 and x=-8. Try to find x which will make us worry!!!!
Answer is in the question

Answer 7

Hint: 1/0 is undefined.

Answer 8

ok @Math4Life I'll give you a hint
What's this?
\[\huge \frac{1}{0}\]

Answer 9

x=-9 and x=-7 are the only points of discontinuities

Answer 10

What values will make the denominator 0? Those are the values where there will be discontinuities.

Answer 11

@ash2326 wait so whats the answer? sorry like I said I was gone

Answer 12

@ash2396 is it x=-9 x=-7?

Answer 13

See my previous post:) Can you create that type of condition here?

Answer 14

@ash2326 is it x=-9 x=-7?

Answer 15

How did you get this?

Answer 16

@ash2326 @eliassaab said so

Answer 17

A rational function is contniuous everwhere except for points that make the denominator zero

Answer 18

@Math4Life just answers won't help. Try to arrive by yourself. If you need any explanation I'm here

Answer 19

everywhere

Answer 20

What's a discontinuity? An asymptote?

Answer 21

@ash2326 Ya I know what your saying I'm just a little confused

Answer 22

@ash2326 I think thats the right answer and if it is can u explain to me how it is?

Answer 23

Okay:)

Answer 24

Rational functions always have a point where they cannot cross called an "asymptote" To find it, set your denominator terms to zero.

Answer 25

@Math4Life Suppose we have a function y given as
\[y=\frac{x-1}{x}\]
as we notice if x=1, numerator is zero.
\[y=\frac{0}{1}=0\]
that's easy to find. No problem at all.:D:D
If we try to plot the graph of y versus x. Then we'll put values of x and find y. It's easy but we don't know about the problem we could face:P

Answer 26

Also remember, in this case, there is a possibility of an oblique asymptote also. To find it, divide your numerator by your denominator.

Answer 27

The quotient will be the oblique asymptote, the remainder will be the distance from the asymptote.

Answer 28

I understand now I just asked a friend

Answer 29

Thanks for all your help people!

Answer 30

@Math4life The most dreadful point is x=0, which will make
\[y=\frac{-1}{0}\]
We can't find its value this is undefined:(:(

Answer 31

See the graph. It confirms that the points of discontinuities are x =-9 and x=-7

Answer 32

@Math4Life now in our question, There are two values of x which will make y undefined. Can you find those two xs?

Answer 33

@ash2326 I understand this now I just talked to a friend over the phone, thanks for all ur help!

Answer 34

Don't forget to find those obliques also.