Question

what is the discontinuity of the function f(x) = x^2-3x-28/x+4

Answer 1

the denominator will tell you ... all you have to do is find the value of x that would make the denominator 0

Answer 2

In this case it's x + 4 = 0
x = -4

Answer 3

hold it don't ........ hmmmmmm I didn't see the numerator until now, if we factor that and it becomes x + 4 above then we can cancel

Answer 4

and then there will be continuous stuff everywhere...sorry I had a rough night

Answer 5

and the discontinuity is a point discontinuity...and not a vertical asymptote

as (x + 4) can be removed as a common factor

Answer 6

yeah I just factored and found out that the x + 4 can be removed. leaving x - 7 behind

Answer 7

and since there's no denominator I don't see how it can be discontinuous. been four years since I touched calc i :P

Answer 8

\[f(x) = \frac{(x-7)(x+4)}{(x +4)}\]

so really you are left with a straight line

f(x) = x - 7

which a point discontinuity

Answer 9

maybe point discontinuity when x = 7?

Answer 10

blah I should get back to my homework sorry to crash T___T

Answer 11

the point discontinuity is at x = -4

Answer 12

hmm I was right earlier.. just leave the equation alone and focus on the denominator.

Answer 13

im still confused

Answer 14

None of what you are saying is an option lol

Answer 15

well look at the denominator as see what makes it zero

x + 4 = 0

this value of x still has relevance ... even though the function can be simplified to a linear function...

you could show this be using a table of values... and the original function



x: -3 -2 -1 0 1 2 3
y -10 -9 -8 -7 -6 -5 -4

so the table of values shows a linear relationship

so what happens when you put x = -4 into the original equation

you get y as undefined...

but if you put x = -4 into

f(x) = x - 7

y = -11


then try x = -5 you get y = -12

so there is a contradiction at x = -4 simplified form it exists... original it doesn't exist

hope it helps

Answer 16

the points of discontinuity are sometimes called a removable discontinuity

here is a link to some notes..

http://classroom.synonym.com/point-discontinuity-algebra-ii-2535.html

my best guess on this question...

you're expected to factor the numerator

remove the common factor

then show that the vertical asymptote doesn't exist...

Answer 17

Yes youve helped thanks :)

Answer 18

Can you help me with another please :P