Question

medal

Answer 1

Hi,
Do you know that you CANNOT divide any number by ZERO?

Answer 2

yes

Answer 3

good!
so in any fraction the denominator cannot become zero.
Ok?

Answer 4

ok

Answer 5

So, in your fraction, could you tell me what is the denominator?

Answer 6

x+4

Answer 7

very good.
For which amount of X it will become Zero?

Answer 8

-4

Answer 9

Nice.
This is the discontinuity point of your function. You got it?

Answer 10

so thats for x but we plug x in to find y ?

Answer 11

No!
You say X=-4 is the discontinuity point of this function.
Ok?

Answer 12

yeah but (-4, ? ) what is y

Answer 13

Y will be INFINITY. that's exactly why it is the discontinuity point.
Do you have a calculator?

Answer 14

my y is an exact number so it cant be infinity

Answer 15

No. Use a calculator to see what will happen if you get so close to X=-4
for example, substitute X=-3.95 now.
I'm waiting to see what Y will be.

Answer 16

wait what do you want me to plug into the calculator

Answer 17

calculate your fraction for these three numbers:
X=-3.95
X=-3.99
X=-3.9999

Answer 18

wait im lost why cant we just use -4

Answer 19

because your calculator gives you an error

Answer 20

yavar, actually there is X+4 on the to as well, so the idea of the limit would tell us that the function is just 2x-3, which correct, but correct only for \(x\ne-4\).

Answer 21

on the "top" too
(correction, grammar)

Answer 22

yes, she doesn't have any idea why X=-4 is discontinuity point.

Answer 23

I mean,
f(x)=(2x-3)(x+4) /(x+4)
(after factoring)

So,
limit x->4\(^{\pm}\)f(x) = 2x-3

Answer 24

I am saying that plugging -3.95 into the function doesn;t work, unles you mean just plugging into the bottom

Answer 25

no i do know why x=-4 but i need to figure out what y is

Answer 26

didn't mean to distract, apologize...

Answer 27

I checked it before but didn't get those factors. I need to sleep. !!!!!!!!!!!!!!!!!!!!!!!

Answer 28

for better idea of discountiuity, it would be better to look at
g(x)=1/(x+4)

Answer 29

(( And by the way, I think she is asking what y of the function would have been, if the function was continuous.... ))

Answer 30

Yes!
Revecca! IT IS 6:10 AM HERE and I've been working for more than 16 hours.
I am so sorry I gave you a wrong answer.

I'm sure @SolomonZelman gives you better advice.

Sorry again and Do great!

Answer 31

The discontinuity point, is the point where the function is not connected.
(one way to interpet "discountimnuity")

Answer 32

thanks for your help though @Yavar

Answer 33

For example, I want to figure out the point of discountinuity of;

\(\color{#000000 }{ \displaystyle f(x)=\frac{(7x+6)(x-5)}{x-5} }\).

I know the function is undefined for x=5,
(because then the denominator =0)

So, we can cancel out (x-5) on top and bottom, and we shall keep in mind the fact that the function does not have a point at x=5.

(when canceling x+5 on top and bottom)
\(\color{#000000 }{ \displaystyle f(x)=7x+6}\)

And
\(\color{#000000 }{ \displaystyle f(5)=7(5)+6=35+6=41}\)

So we know that the point of discountinuity is (5,41)....

Answer 34

but with my problem there is no perfect binomial to split it up into

Answer 35

\(2x^2+5x-12=(2x-3)(x+4) \)

Answer 36

So, in your case the function is

\(\color{#000000 }{ \displaystyle f(x)=\frac{(2x-3)(x+4)}{x+4} }\).

and you need to determine the point of discountinuity.

Answer 37

-3+4 doesnt equal 5

Answer 38

???

Answer 39

I don't really understand where -3+4 is coming from

Answer 40

but,
-3+4•2=5

Answer 41

and the factoring is correct....

Answer 42

ohhhhhhhhhhhhhhhhhhhhhhh i see thanks

Answer 43

thats why it has been so confusing you need to multiply that number by it

Answer 44

Ok, you want to determine the discontinuity point of

\(\color{#000000 }{ \displaystyle f(x)=\frac{(2x-3)(x+4)}{x+4} }\).

And, as you said the function is not continuous at x=-4,
So once you know noted that x\(\ne\)-4,

you can cancel the (x+4)'s out, and to then evaluate the function at x=-4, to find the y-coordinate of this point of discountinuity (once you have already known that the x-coordinate of point of discountinuity is =-4).

Answer 45

ok then to figure out what y is you plug -4 into the finished product which is (2x-3) so 2x(-4)-3 giving you -11 so your discontinuity is at (-4, -11)

Answer 46

yes, the point of discountinuity is (-4,-11).
Fabulous!

Answer 47

yayyyy but now i have to find the zeros

Answer 48

the zeros, (or the x intercepts)...

Answer 49

i have to find what the zeros of the function are

Answer 50

when you are finding the zeros, you are actually going to have to cancel (x+4)'s on top and bottom , i.e. to deal with

f(x)=2x-3

At what value(s) of x, is f(x) going to be equal to 0?

Answer 51

-3/2

Answer 52

but i need to find the other zero bc there is 2

Answer 53

Actually, there is only 1 zero, because at x=-4, the function does NOT have an x-intercept.

Answer 54

you found the zero incorrectly.
x=-3/2 is not the "zero"

Answer 55

where is the zero at

Answer 56

f(x)=2x-3
0=2x-3
x=?

Answer 57

x=3/2 @SolomonZelman

Answer 58

yes

Answer 59

(and that is the only zero there is to the function)

Answer 60

i dont understand why y is 0

Answer 61

f(3/2)=2(3/2)-3=3-3=0

Answer 62

ohok thank you for navigating through my cluelessness, you helped a lot

Answer 63

yw