Mathematics 29 Online
OpenStudy (anonymous):

Range of 5/(x-3)

OpenStudy (amistre64):

its got a va at 3 so id assume the range is all up and down

OpenStudy (amistre64):

except for 0 maybe

jimthompson5910 (jim_thompson5910):

The horizontal asymptote is y = 0, so this is the only output value that y cannot equal is 0 So the range is the set of all real numbers but y cannot equal 0

OpenStudy (amistre64):

kinda hard to equal 0 when you got a constant up top :)

jimthompson5910 (jim_thompson5910):

no, if the degree of the denominator exceeds the degree of the numerator, then the horizontal asymptote is always y = 0

jimthompson5910 (jim_thompson5910):

I'm not doing equating of any kind, I'm finding the horizontal asysmptote

OpenStudy (amistre64):

well yeah, if you wanna go by rules and not logic...

OpenStudy (amistre64):

.... that was peculiar statement; since the rules are founded on logic ;)

OpenStudy (amistre64):

5/x = 0 when 5 = 0, so never

OpenStudy (anonymous):

did asymptotes last year and cannot remember them. how do you fing the horizantal asymptote

jimthompson5910 (jim_thompson5910):

logically, this is explained by the fact that the degree has a higher rate of growth, so as x approaches infinity, the denominator will be much much larger than the numerator So this means we'll have a very small fraction (when x --> oo)

jimthompson5910 (jim_thompson5910):

ideally, calculus is needed to see this, but you can see this visually too

OpenStudy (amistre64):

3 simple rules for HA bottom bigger than top; 0 bottom = top; leading coeffs bottom smaller than top; divide out and toss the remainder

jimthompson5910 (jim_thompson5910):

oops meant to write "denominator has higher rate of growth"

jimthompson5910 (jim_thompson5910):

exactly, so what's the issue?

OpenStudy (amistre64):

march 1984 SI edition of sports illustrated

OpenStudy (amistre64):

OpenStudy (anonymous):

just to butt in at the last minute, not sure calc is needed. it is pretty clear that $\frac{5}{x-3}$ is never 0 since a fraction is only 0 if the numerator is

jimthompson5910 (jim_thompson5910):

it approaches zero though as x approaches infinity

OpenStudy (anonymous):

k... thanks

OpenStudy (amistre64):

now now, i think we might need calculus to determine this for us; lets see what leibniz and newton are up to these days :)

jimthompson5910 (jim_thompson5910):

they'll fight to the death like they did 300 yrs ago...so idk if they'll be of much help lol

OpenStudy (amistre64):

lol ... :)

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