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its pretty difficult
oh okay listen there is a simple way of doing these
without cheating -_-
factor thjis x^2-2x-3
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
if u set x=3 that turns one of those brackets into 0 so u have 2/(0*something)=2/0
can u think of another number u can set x to to make the denominator 0
yep thats that -1+1 =0 so
so setting x=3 or x=-1 make the denominator 0 this means x cannot equal these numbers
there are no other numbers that can turn the denominator 0
so all other values of x are okay
so your domain is simply x is not equal to 3 or -1 and x is every other real number
your range is -infinity to infinity as y can be almost anything
i mean y can be everything not almost
okay carry on the work
what point should i graph?
find the x and y intercepts, find the vertical asymtototes then u will be ready to graph
oh wait there is actually a number y canot equal which is 0
what point do you recommend i graph?
y=0 means what is x?
no think about this
lets say y=1/x y=0=1/x what does x have to be to make this fraction 0
1/1 = 1
that doesnt make 0 try again
1/-1 = -1
what happens when x is a big number 1/1=1 1/10=0.1 1/1000000=0.0000001
the bigger the x the closer u are getting to 0
so wha do u think x has to be
very similiar to ur question
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?
sorry, im a little confused
thats the intercept
we saw that when it was something like 0=2/B lets say B has to be infinity
okay so what values of x make the bottom infity or negative infinity
yep and x can also be negative infinity
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
y=0 is a horizontal asymtote
ill leave it up to you to find the vertical asymtotes now
or you could use - infinity