Question

Domain and range of (1/((x-1)^2))+3 would be?
Equations of the asymptotes of ((7x^2)-3)/((7x^2)+3) are?
I'm having trouble remembering how to do these since we learned it so long ago.

Answer 1

domain and range... graph the function (mentally or on your calculator) domain is X, range is Y
asymptotes, vertical is where the denominator = 0, horizontal exists if the function goes to the same value as x -> ± infinity

Answer 2

sound familiar?

Answer 3

yeah I remember what they are; looking at the first one I want to say the domain would be (-∞,1) U (1, ∞) and the range would be (3, ∞) but I feel like I'm wrong.

Answer 4

did you graph it?

Answer 5

yes

Answer 6

This is the graph I got from graphing it on WolframAlpha

Answer 7

you're right

Answer 8

Thank you!! I was really confused on it so I'm glad I was doing it right!

Answer 9

(a nice online graphing calculator: https://www.desmos.com/calculator)

Answer 10

Thanks, I'll be using that! :)

Answer 11

sorry, at first I thought it was wrong because I was looking at the second equation

Answer 12

now the second part?

Answer 13

For the second one I put that the HA was 1 and the VA was √(-3/7) but I know that one of those is incorrect and I can't remember how to calculate it.

Answer 14

your HA is right. Look at the denominator (the bottom half) of the fraction again. You have an asymptote when that part = 0. You found the way to make it equal 0, but the trick is that that isn't a real number. Square roots of negative numbers are complex numbers.

Answer 15

so would you use i and say i√(3/7)

Answer 16

it's squared and the square root operation implies a positive result, so your teacher might want you to specify that it is ±i√(3/7)

Answer 17

thank you!

Answer 18

you're welcome