Question

Show all work to identify the asymptotes and zero of the function f of x equals 3 x over quantity x squared minus 9.

I HAVE BEEN TRYNA DO THIS PROBLEM BY MYSELF FOR 3 DAYS NOW KAN SUMONE PLZ HELP

Answer 1

\( f(x) = \dfrac{3x}{x^2 - 9}\)

is this it?

Answer 2

yes

Answer 3

The vertical asymptotes can be found when you set the denominator = 0

do you know how to factor \( x^2 - 9\)

hint:
\( a^2 - b^2 = (a+b)(a-b)\)

Answer 4

no i dont know nun of dis stuff,,she said if we kan answer this question she will give us bonus points,,but we never did this math

Answer 5

But can you factor \( x^2 - 9\)

hint:
\( 9 = 3^2\)

Answer 6

ion rlly kare about the points but i juss wanna see how to do it for future problems

Answer 7

So tell her that to find the vertical asymptote, you have to set the denominator equal to 0

and once you factor x^2 - 9, you'll have your answer in no time

Answer 8

and then the bonus points shall be yours, my friende

Answer 9

(x-3) (x+3)

Answer 10

Perfect!!

so remember we said we're setting the denominator equal to 0

(x^2 - 9) = 0

(x+3)(x-3) = 0

so now we have

x + 3 = 0
and
x - 3 = 0

what two numbers do you get when you solve for x?

Answer 11

-3 and 3???

Answer 12

Yes~
Which means that x cannot equal -3 or 3, so they are your asymptotes

Answer 13

Exactly! So those are your asymptotes

x = 3
and x = -3

keep the x equals to part

Answer 14

Now we have one last thing- we need to find the zeroes of the function

Answer 15

wat is dat

Answer 16

Zeroes are like the x-intercepts

Answer 17

the zero of the function is the x-intercept which is when y = 0

so take a look at your function and put y = 0

\( 0 = \dfrac{3x}{x^2 -9}\)

to make it equal to 0, we need the NUMERATOR to equal 0
if the denominator equals 0 then it would be undefined

so what times 3 will give you 0?

Answer 18

0

Answer 19

So that's the zero of your function! On the graph, it would be when it crosses the x-axis at (0, 0)

Answer 20

you can see the asymptotes as x = -3 and x = 3
https://www.desmos.com/calculator/ikl8cvsnq6

Answer 21

thanx

Answer 22

You're welcome!