Question

please help!!! greatly appreciated! The vertical asymptote of the function y=log(x+3)-8 is a. x=-3 b. x=3 c. x=8 or d. x=-8

Answer 1

this shifts the function to the left 3 units so vertical asymptote shifts from \(x=0\) to \(x=-3\)

Answer 2

thank you so much!!

Answer 3

and can somebody help me find the range and domain of the function y=ln(x-1)+2

Answer 4

If you think about the logarithm and where it disappears / is no longer defined, its basically when the input is equal to 0, log 0 is not defined. So we could also set x + 3 = 0. :)

Answer 5

thank you so much @AccessDenied

Answer 6

so did you get -3 for the answer also then?

Answer 7

Yep. :)

As for that second q, the domain is once again the points where the input is greater than 0.
We could simply set 'x - 1>0' here for those values. Once we hit 0, we get another asymptote and then the graph vanishes. :)

In this case, the range is usually just all real numbers. It gets very very small (large/negative) as it approaches its asymptote, and it gets larger and larger as you go bigger and bigger values.

Answer 8

thank you so much

Answer 9

You're welcome! :)

Answer 10

so what is the domain for that question?

Answer 11

i wish i could give you best answer but i have already given it for this question so i can ask another one and give you best answer there? :)

Answer 12

y = ln(x - 1) + 2
--> ln is only defined where x - 1 > 0. We just solve this inequality for the domain.

Answer 13

so the domain is 1, ∞?

Answer 14

or (-1,∞)

Answer 15

x - 1 > 0 add 1 to both sides:
x > 1 So (1, infinity) is correct. :)

Answer 16

thank you so much again!!!! xx