new question. :)
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 :)
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Let me rearrange before my brain explodes..
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What do u call this type of function again?
Bracket assassin?
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.
Then it wouldn't need much messy algebra.
Wait, let me do it.
sure
Wait, this is embarrassing question but do I need to expand the denominator first?
No. Half of it is already simplified with the (7-x). Do you remember the rule for a^2 - b^2 ?
O eye see
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.
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Like dat?
Close, recall that there are two solutions to the x^2 - 1 because it's to the second degree
You're missing one more x value
x^2 = 1 x = sqrt(1) sqrt(1) can be 1 and also ...
Negative 1
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Yes, so you now have your domain.
That’s it? Noice
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
yes
How do we go about solving the VA in this case? Since it’s in factored form...
You already got your VA, it was the x values you obtained.
Because if you plug in those x values, there would be a 0 in the denominator. That would make the output undefined.
But I though those were the domains no? Sorry
Yuhh I forgot about that. Thanks.... so how do we find the range?
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
You found the range with the HA.
Okie dokie...
I need a food break brb ;)
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