help please :) What is the domain and range of (4x+3)/x^2-1

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help please :) What is the domain and range of (4x+3)/x^2-1

Mathematics
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the domain is all real numbers but -1 and 1 right??
yeah since there is a fraction. we have a restriction so \[(x^2-1) =(x+1)(x-1) \] x=1, -1 so our domain should be all reals except when x =-1 or x = 1. Those restrictions create a blank space in the graph
what about range?

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range is in the y-axis... hmm.
range is always a pain >_< but here's the graph of the function
i don't get it :/
we have the domain... which x is all reals except when x =1 and x =-1
we got the graph of the function ... the range is in the y-axis so it must be all reals except when y is some number ?!
@jim_thompson5910 I need to refresh my memory. Range is in the y-axis but how do we find it again when there are restrictions in the function ?
degree of denominator = 2 degree of numerator = 1 since (degree of denominator) > (degree of numerator), this means y = 0 is a horizontal asymptote. So y = 0 would be kicked out of the range but y = 0 is certainly possible. Just let x = -3/4
?!
plug in x = -3/4 and you'll get y = 0
so the range is the set of all real numbers
how is the range all reals? I don't get that part..
oh wait.. unless the line is going through all y -values. ._.
yeah any y value is possible
wait i don't get it
it is all reals XD . My mind went blank . Why is domain easier to find than range?
in the graph the lines is going through all the y-values where as in the x-values, there is a break (like an empty space) at x=1, x = -1
oh!! i see it, thank you :) can you also help me on finding the relative extrema for 2x^3+5x^2-25x?
alright but first we have to graph this
can we find it without graphing
relative extrema.. like maxs and mins.. (gonna be hard though without a graph )
there's the first derivative test though for increasing and decreasing.. finding extremas... but I'm not sure if you're at that level yet.
nope haha im confused. i'm supposed to find it without equation i think
without the graph*
so you're not in a calculus course?
its precalc!
ok... do you know how to take derivatives?
weird you need those
this site has an example for finding relative extrema http://ltcconline.net/greenl/courses/105/theoremsrelatedrates/extrema.htm
i figured it out haha thanks :)

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