Question

Identify the horizontal asymptote of f(x) = 3 over 5 x.

y = 3 over 5

y = 0

y = 5 over 3

No horizontal asymptote

Answer 1

So the horizontal asymptote is what we see when we let 'x' approach infinity.

so with \(\large f(x) = \frac{3}{5x}\) when we let x = infinity, what does the function approach?

Answer 2

i dont really know ...sorry :/

Answer 3

That's alright, here we'll do something quick so you can see

what does 1/10 equal?
what does 1/100 equal?
what does 1/1000 equal?

etc...

as you make the denominator larger and larger, what does the result seem to do??

Answer 4

get bigger.

Answer 5

@johnweldon1993

Answer 6

Not quite

1/10 = .1
1/100 = .01
1/1000 = .001
1/10000 = .0001

It would see that as the denominator gets bigger and bigger, the result gets closer and closer to 0 right?

Answer 7

right!

Answer 8

@johnweldon1993

Answer 9

And that same thing happens in our question here

\[\large f(x) = \frac{3}{5x}\]

as x gets bigger and bigger, the denominator does too, thus this equation approaches 0

Answer 10

wait so its a ?

Answer 11

No its B, The horizontal asymptote is 0