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System Message

[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Lily (Customer)

[00:00:00] f(X)= (7/6)^x Vertical asymptote= horizontal asymptote= x-intercept=
Thanks!

Sam B (Tutor)

[00:00:07] Welcome to Tutor.com !
Let's get started.

Lily (Customer)

[00:00:22] hi!

Sam B (Tutor)

[00:00:28] So all we're trying to do is find the vertical and horizontal asymptotes, as well as the x-intercept.
Is that correct?

Lily (Customer)

[00:00:31] yes

Sam B (Tutor)

[00:01:03] Great!
Which one would you like to start with first?

Lily (Customer)

[00:01:09] vertical asymptote

[00:01:15] i have no idea how to set it up

Sam B (Tutor)

[00:01:33] Okay, no problem.
Do you happen to know what a vertical asymptote is?

Lily (Customer)

[00:02:22] yes, kind of. I know it is where the line starts changing. I knw that it normally is where the denominator equals 0, but that is it

Sam B (Tutor)

[00:04:04] That's good!
And in this function, can we ever have a denominator of zero?

Lily (Customer)

[00:04:17] no

Sam B (Tutor)

[00:04:43] Exactly!
So can this function have a vertical asymptote?

Lily (Customer)

[00:05:09] i guess not?

Sam B (Tutor)

[00:05:21] Perfect :)

[00:05:39] Now let's look at horizontal asymptotes.
Do you happen to know how to find them?

Lily (Customer)

[00:05:59] no. all i knew was end behavior asymptotes

[00:06:11] i have never seen these before.

Sam B (Tutor)

[00:06:35] Okay, that's fine.
A horizontal asymptote is basically an imaginary horizontal line that our function can never cross.

Lily (Customer)

[00:06:48] ok

Sam B (Tutor)

[00:06:57] Since we have an exponential function, there is a certain number that our function can never be less than.
Do you happen to know what that number is?

Lily (Customer)

[00:07:23] 0?

[00:07:26] or 1

Sam B (Tutor)

[00:07:39] Zero is exactly right.
If we were to graph it, it would look something like this:

[00:08:19] An exponential function can never be less than or equal to 0, so our horizontal asymptote must be at y=0.
Does that make sense?

Lily (Customer)

[00:08:50] yes

Sam B (Tutor)

[00:09:17] Awesome!
So now let's look at our x-intercept.
What does "x-intercept" mean exactly?

Lily (Customer)

[00:09:48] where y is zero. and where it crosses the x-axis. which it can't, right?

Sam B (Tutor)

[00:10:10] Absolutely!
Since our function can't cross y=0, it can't have an x-intercept.

[00:10:18] Good job :)

Lily (Customer)

[00:11:02] so if you had g(X)=10^-x, your vertical asymptote would be NONE also? you can't have one, right?

Sam B (Tutor)

[00:11:40] Yup.
Since we still have an exponential function, we still won't have a vertical asymptote, because we don't have any cases where our denominator can be zero.

Lily (Customer)

[00:12:34] so you will NEVER have a vertical symptote for an exponential function?

Sam B (Tutor)

[00:13:00] For these types of exponential functions, I don't believe we will ever have a vertical asymptotes.

[00:13:07] asymptote*

Lily (Customer)

[00:13:08] great to know!

[00:13:11] :)

Sam B (Tutor)

[00:13:22] Cool!
Was there anything else you needed help with?

Lily (Customer)

[00:13:40] that is it. i will probably sign back on soon for help with more homework. Thnks though :)

Sam B (Tutor)

[00:13:50] My pleasure!

[00:13:52] Thanks for using Tutor.com.Â Please fill out the survey as you leave so we can learn how we can better help you in the future!Â

Lily (Customer)

[00:13:58] sure

[00:14:00] BYE

Sam B (Tutor)

[00:14:02] Bye :)