please help

- anonymous

please help

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- anonymous

##### 1 Attachment

- just_one_last_goodbye

brb

- anonymous

its pretty difficult

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- just_one_last_goodbye

http://i.imgur.com/2kS2IGy.png

- anonymous

##### 1 Attachment

- dan815

oh okay listen there is a simple way of doing these

- dan815

without cheating -_-

- anonymous

sorry lol

- dan815

factor thjis x^2-2x-3

- anonymous

(x-3)(x+1)

- dan815

ok right

- dan815

now the denominator in a fraction cannot be 0 because we dont know what 1/0 really is it can be infinity or - infinity or what

- dan815

|dw:1440461633780:dw|

- dan815

if u set x=3 that turns one of those brackets into 0 so u have 2/(0*something)=2/0

- dan815

can u think of another number u can set x to to make the denominator 0

- anonymous

-1?

- dan815

yep thats that -1+1 =0 so

- dan815

so setting x=3 or x=-1 make the denominator 0 this means x cannot equal these numbers

- anonymous

ok

- dan815

there are no other numbers that can turn the denominator 0

- dan815

so all other values of x are okay

- dan815

so your domain is simply x is not equal to 3 or -1 and x is every other real number

- dan815

your range is -infinity to infinity as y can be almost anything

- dan815

i mean y can be everything not almost

- anonymous

ok

- anonymous

thank you

- dan815

okay carry on the work

- anonymous

what point should i graph?

- dan815

find the x and y intercepts, find the vertical asymtototes then u will be ready to graph

- dan815

oh wait there is actually a number y canot equal which is 0

- anonymous

what point do you recommend i graph?

- dan815

y=0 means what is x?

- anonymous

0

- dan815

no think about this

- dan815

lets say y=1/x
y=0=1/x what does x have to be to make this fraction 0

- anonymous

1

- dan815

1/1 = 1

- anonymous

0

- dan815

that doesnt make 0 try again

- anonymous

-1

- dan815

1/-1 = -1

- dan815

what happens when x is a big number
1/1=1
1/10=0.1
1/1000000=0.0000001

- dan815

the bigger the x the closer u are getting to 0

- dan815

so wha do u think x has to be

- anonymous

infinity?

- dan815

yes

- dan815

very similiar to ur question

- dan815

y=0=2/((x-3)(x+1))
now the denominator has to be infinity for y=0
so (x-3)(x+1) = inf what is x to make this true?

- anonymous

2?

- anonymous

sorry, im a little confused

- dan815

okay look

- dan815

|dw:1440462385204:dw|

- anonymous

thats the intercept

- dan815

we saw that when it was something like
0=2/B lets say
B has to be infinity

- anonymous

ok

- dan815

|dw:1440462433939:dw|

- anonymous

ohhhhhhh ok

- dan815

okay so what values of x make the bottom infity or negative infinity

- anonymous

infinity

- dan815

yep and x can also be negative infinity

- dan815

so this graphy will actually never have a y intercept as there is no real x value where the graph will intersect the y=0 line

- dan815

y=0 is a horizontal asymtote

- dan815

ill leave it up to you to find the vertical asymtotes now

- anonymous

x=+infinity

- anonymous

or you could use - infinity

- anonymous

:W

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