Question

State the horizontal asymptote of the rational function.

f(x) = quantity nine x squared minus three x minus eight divided by quantity four x squared minus five x plus three.

y = 3/5

y = 9/4

y = 0

None

Answer 1

for any x value, the terms 9x^2 and 4x^2 will give you a number much bigger than any other term, right?

Answer 2

as we pick larger and larger values of x

Answer 3

@yreanne ?

Answer 4

Sorry. Thanks for replying.

Answer 5

did you get the answer?

Answer 6

No. I am not sure how to solve the problem.

Answer 7

When you say larger term...what do you mean?

Answer 8

to find the horizontal asymptote we have to think as x approaches positive and negative infinity

Answer 9

Okay...

Answer 10

so, let's say x=100, 9(x)² is much larger than -3(x)

Answer 11

the same for the expression on the denominator, 4(x)² and -5(x)

Answer 12

because 9x² and 4x² increases really faster as x increases you can ignore the other terms

Answer 13

so the function 'becomes' 9x² / 4x²

Answer 14

simplifying you get 9 / 4

Answer 15

So it just becomes 9/4?

Answer 16

yeah

Answer 17

Thanks. So for every horizontal problem thats what I would do?

Answer 18

you can do it this way or calculating some points, like f(1), f(10), f(100), you will see the same thing, the function f(x) will approach some value

Answer 19

as x increases

Answer 20

or decreases, neg. infinity

Answer 21

Okay. Thanks again.

Answer 22

you're welcome

Answer 23

Do you mind helping me with another one please?

Answer 24

let's see if I can do it, what is it?

Answer 25

Give an example of a rational function that has no horizontal asymptote and a vertical asymptote at
x = 1.

Answer 26

you have to write a function for this?

Answer 27

No. I just have to figure out an equation that has no horizontal asymptote and a vertical asymptote at x=1

Answer 28

well, vertical asymptote are when the rational expression is undefined, the denominator is equal to 0, so if it has ti be at x=1, the denominator can be
(something) / x-1

Answer 29

So anything over x-1?

Answer 30

for the vertical asymptote condition, now for the no horizontal asymptote I have to think about it

Answer 31

Could it just be zero over x-1

Answer 32

I don't know, this is a horizontal straight line with a hole at x=1, not sure =/

Answer 33

Okay. Thank you so much for your time and effort.

Answer 34

ok, hope somebody else can help you

Answer 35

Thanks again.