What are the points of discontinuity? Are they all removable?
y=(x+4)/(x^2+5x+4)

Question

What are the points of discontinuity? Are they all removable?
y=(x+4)/(x^2+5x+4)

johnweldon1993 · Answer

Hint* think about how you can factor the denominator

juan1857 · Answer

(x+4)(x+1)

welshfella · Answer

so now we can simplify  the function

juan1857 · Answer

so would it be 1/(x+1)?

welshfella · Answer

right 
so where would there be a discontinuity in the graph of this function?

juan1857 · Answer

-1?

welshfella · Answer

yes

welshfella · Answer

it looked like there was another one at x = -4 but since  the (x + 4) cancelled out its was removed.

welshfella · Answer

there's a discontinuity at x = -1

juan1857 · Answer

ok, so how do you know if it is removable?

welshfella · Answer

welshfella · Answer

I guess because we could remove it!

juan1857 · Answer

so is that the only point of discontinuity?

welshfella · Answer

to be honest I haven't come across that expression 'removable discontinuity' before , that's why im sort of guessing....

juan1857 · Answer

oh ok

welshfella · Answer

Yes just one point of discontimuity

welshfella · Answer

as you see Desmos gives that as the graph of the original function

juan1857 · Answer

alright, Thanks

welshfella · Answer

yw

juan1857 · Answer

still need help with finding if it is removable

marcelie · Answer

hmm i think it would be removal at x= -4 ?

satellite73 · Answer

yes, because when you factor and cancel you are removing it

juan1857 · Answer

oh so 1, isn't a removable?

satellite73 · Answer

nope

satellite73 · Answer

the finished product is $$\frac{1}{x+1}$$so the discontinuity at $-1$ is still there

marcelie · Answer

well ik this is not the right term to say it but whenever you see the same factor that cancels out that would be your removable

satellite73 · Answer

sounds right to me

juan1857 · Answer

so you always get the opposite sign ?

marcelie · Answer

oh okay x) its been awhile havent seen this lol

satellite73 · Answer

$$\frac{x+4}{(x+1)(x+4)}$$ now you see it (the discontinuity at -4
$$=\frac{1}{x+1}$$ now you don't

satellite73 · Answer

as for the "opposite sign" when you set $$x+1=0$$ and solve you get $x=-1$

juan1857 · Answer

so for the removable you get the opposite sign too?

juan1857 · Answer

because it was (x+4) so it should be -4, to make it 0, right?

juan1857 · Answer

because it was (x+4) so it should be -4, to make it 0, right?

marcelie · Answer

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