anonymous
  • anonymous
help please :) What is the domain and range of (4x+3)/x^2-1
Mathematics
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
the domain is all real numbers but -1 and 1 right??
UsukiDoll
  • UsukiDoll
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
anonymous
  • anonymous
what about range?

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UsukiDoll
  • UsukiDoll
range is in the y-axis... hmm.
UsukiDoll
  • UsukiDoll
range is always a pain >_< but here's the graph of the function
anonymous
  • anonymous
i don't get it :/
UsukiDoll
  • UsukiDoll
we have the domain... which x is all reals except when x =1 and x =-1
UsukiDoll
  • UsukiDoll
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 ?!
UsukiDoll
  • UsukiDoll
@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 ?
jim_thompson5910
  • jim_thompson5910
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
UsukiDoll
  • UsukiDoll
?!
jim_thompson5910
  • jim_thompson5910
plug in x = -3/4 and you'll get y = 0
jim_thompson5910
  • jim_thompson5910
so the range is the set of all real numbers
UsukiDoll
  • UsukiDoll
how is the range all reals? I don't get that part..
UsukiDoll
  • UsukiDoll
oh wait.. unless the line is going through all y -values. ._.
jim_thompson5910
  • jim_thompson5910
yeah any y value is possible
anonymous
  • anonymous
wait i don't get it
UsukiDoll
  • UsukiDoll
it is all reals XD . My mind went blank . Why is domain easier to find than range?
UsukiDoll
  • UsukiDoll
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
UsukiDoll
  • UsukiDoll
anonymous
  • anonymous
oh!! i see it, thank you :) can you also help me on finding the relative extrema for 2x^3+5x^2-25x?
UsukiDoll
  • UsukiDoll
alright but first we have to graph this
anonymous
  • anonymous
can we find it without graphing
UsukiDoll
  • UsukiDoll
relative extrema.. like maxs and mins.. (gonna be hard though without a graph )
UsukiDoll
  • UsukiDoll
UsukiDoll
  • UsukiDoll
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.
anonymous
  • anonymous
nope haha im confused. i'm supposed to find it without equation i think
anonymous
  • anonymous
without the graph*
UsukiDoll
  • UsukiDoll
so you're not in a calculus course?
anonymous
  • anonymous
its precalc!
UsukiDoll
  • UsukiDoll
ok... do you know how to take derivatives?
UsukiDoll
  • UsukiDoll
weird you need those
UsukiDoll
  • UsukiDoll
this site has an example for finding relative extrema http://ltcconline.net/greenl/courses/105/theoremsrelatedrates/extrema.htm
anonymous
  • anonymous
i figured it out haha thanks :)

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