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Mathematics 32 Online
Ballery1:

new question. :)

Ballery1:

don't know what type of function this is but we need to find the domain and range of this beast....if there're any asymptotes or restrictions....let me know :)

Ballery1:

|dw:1560646213154:dw|

Ballery1:

Let me rearrange before my brain explodes..

Ballery1:

|dw:1560646260606:dw|

Ballery1:

What do u call this type of function again?

Ballery1:

Bracket assassin?

Ferredoxin4:

This is just another rational function with a 3rd degree polynomial in the denominator. It doesn't really matter the name. To find vertical asymptotes, just set the denominator terms to 0 and find x. I'd suggest simplifying that difference of squares binomial then using the zero product property to find the x values.

Ferredoxin4:

Then it wouldn't need much messy algebra.

Ballery1:

Wait, let me do it.

Ferredoxin4:

sure

Ballery1:

Wait, this is embarrassing question but do I need to expand the denominator first?

Ferredoxin4:

No. Half of it is already simplified with the (7-x). Do you remember the rule for a^2 - b^2 ?

Ballery1:

O eye see

Ferredoxin4:

Yes. Apply that to the different of squares binomial and make them simpler binomials. Then apply the zero product property and you'll find the x values.

Ballery1:

|dw:1560646783379:dw|

Ballery1:

Like dat?

Ferredoxin4:

Close, recall that there are two solutions to the x^2 - 1 because it's to the second degree

Ferredoxin4:

You're missing one more x value

Ferredoxin4:

x^2 = 1 x = sqrt(1) sqrt(1) can be 1 and also ...

Ballery1:

Negative 1

Ballery1:

|dw:1560647042854:dw|

Ferredoxin4:

Yes, so you now have your domain.

Ballery1:

That’s it? Noice

Ballery1:

Correct me if I’m wrong for the range but since the leading degree in the numerator is smaller than the degree in the denominator...the HA is y=0

Ferredoxin4:

yes

Ballery1:

How do we go about solving the VA in this case? Since it’s in factored form...

Ferredoxin4:

You already got your VA, it was the x values you obtained.

Ferredoxin4:

Because if you plug in those x values, there would be a 0 in the denominator. That would make the output undefined.

Ballery1:

But I though those were the domains no? Sorry

Ballery1:

Yuhh I forgot about that. Thanks.... so how do we find the range?

Ferredoxin4:

Same thing. Domain is the entire value of the x set considering the VA. Rnage is the entire value of the y set considering the HA

Ferredoxin4:

You found the range with the HA.

Ballery1:

Okie dokie...

Ballery1:

I need a food break brb ;)

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