Question

help with calculus ! f(x)= x/(lx^2-9l) What is the domain? i also have to write an equation for each vertical & horizontal asymptote

Answer 1

To find the domain... remember that the denominator can not be equal to zero, so find where it's equal to zero.

Answer 2

Oh okay . so just make the denominator = to 0? and figure it out from there?

Answer 3

Yep

Answer 4

There's only two x values that give a denominator of zero.

Answer 5

okay thanks! do you know how to write an equation for each horizontal & vertical asymptote?

Answer 6

Vertical asymptotes will be the same as the x values that make the denominator zero.

Horizontal is a bit more complex... you want to look at the highest powers on the numerator and denominator.

Answer 7

how would i write them as an equation tho?

Answer 8

x = ...

y = ...

Answer 9

so when you say power you mean x^2 . so the highest power will be 2?

Answer 10

Yep. Highest power on the top is x. On the denominator is |x^2|

Do you know what happens to y= x/|x^2| as x approaches infinity? what will y approach?

Answer 11

No . i'm not sure. my teacher tried explaining this to me but i could not grasp what he was telling me

Answer 12

does y get closer to 0?

Answer 13

Yes... x/x^2 simplifies to 1/x... which when x is huge, 1/(huge number) is ~zero

as x approaches neg infinity, same thing, y approaches zero

Answer 14

for example: https://www.google.com/search?q=1%2F10000000000&oq=1%2F10000000000&aqs=chrome..69i57j69i58j0.2651j0j7&sourceid=chrome&espv=210&es_sm=93&ie=UTF-8#es_sm=93&espv=210&q=1%2F1000000&safe=off

Answer 15

as x gets larger, 1/x gets closer to zero

Answer 16

oh okay. ty

Answer 17

Always helps to use a graph to confirm it https://www.google.com/search?q=1%2F10000000000&oq=1%2F10000000000&aqs=chrome..69i57j69i58j0.2651j0j7&sourceid=chrome&espv=210&es_sm=93&ie=UTF-8#es_sm=93&espv=210&q=x%2FABS(x%5E2-9)&safe=off