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

- anonymous

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

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- anonymous

the domain is all real numbers but -1 and 1 right??

- 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

what about range?

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- UsukiDoll

range is in the y-axis... hmm.

- UsukiDoll

range is always a pain >_<
but here's the graph of the function

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- anonymous

i don't get it :/

- UsukiDoll

we have the domain... which x is all reals except when x =1 and x =-1

- 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

@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

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

?!

- jim_thompson5910

plug in x = -3/4 and you'll get y = 0

- jim_thompson5910

so the range is the set of all real numbers

- UsukiDoll

how is the range all reals? I don't get that part..

- UsukiDoll

oh wait.. unless the line is going through all y -values. ._.

- jim_thompson5910

yeah any y value is possible

- anonymous

wait i don't get it

- UsukiDoll

it is all reals XD . My mind went blank . Why is domain easier to find than range?

- 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

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- anonymous

oh!! i see it, thank you :)
can you also help me on finding the relative extrema for 2x^3+5x^2-25x?

- UsukiDoll

alright but first we have to graph this

- anonymous

can we find it without graphing

- UsukiDoll

relative extrema.. like maxs and mins.. (gonna be hard though without a graph )

- UsukiDoll

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- 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

nope haha im confused. i'm supposed to find it without equation i think

- anonymous

without the graph*

- UsukiDoll

so you're not in a calculus course?

- anonymous

its precalc!

- UsukiDoll

ok... do you know how to take derivatives?

- UsukiDoll

weird you need those

- UsukiDoll

this site has an example for finding relative extrema
http://ltcconline.net/greenl/courses/105/theoremsrelatedrates/extrema.htm

- anonymous

i figured it out haha thanks :)

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