Question

What is the equation of the vertical asymptote of the graph of f(x) = 2 log3(x + 1) 3?

Answer 1

shuold be x = -1

Answer 2

is that an exponent of 3 on the end?

Answer 3

It is a sub unit of 3

Answer 4

I'm trying to make quiz corrections in my math class and I had this one wrong :/

Answer 5

the answer IS -1 but I don't understand how

Answer 6

what were the choices?

Answer 7

all graphs of logs.... at least normal logs.... never reach zero or negative numbers;

any modification of them tends to keep that same trait.

when they shift the graph by (x+1) they modify the x component so that it reads x = -1

Answer 8

Okay, so why would the correct answer choice be -1? I didn't understand it

Answer 9

When you say that the graph is shifted by (x + 1), how does the x component GET modified, could you explain that?

Answer 10

i can try :)

all graphs are examined at the origin at (0,0)

Answer 11

that is the easiest place to examine them up close and personal like; when they are NOT at the origin we have to move them..

Answer 12

Right

Answer 13

if the graph is at (x=-1)... we write ourselves a note to tell us where we got it from; or rather, how far we had to move it and in what direction to get it to (0,0)

Answer 14

that way we can put it back when we are done looking at it.

if the graph is at x=-1; how far and in what direction did we have to move it to get it to the origin?

Answer 15

we'd move it 1 place to the right, correct?

Answer 16

that correct; we move the "x" by +1. So we write ourselves a note (x+1); so we can put it back when we are done right?

Answer 17

Okay

Answer 18

suppose x=3 originally; what is our note look like then?

Answer 19

3 + 1 = 4

Answer 20

think about that again; how far and in what direction do we need to move the graph from x=3 to get it to the origin (0)? if we add (+1) to it it gets us to 4... not to zero.

Answer 21

so if x = 3, how far to the origin? that would be 3 units to the left, -3

Answer 22

correct :) so our note becomes (x-3) to remind ouselves where we got it from.

Answer 23

Okay

Answer 24

so your problem; the log is normally at x = 0 with an Vasymptote of x=0

Answer 25

but they got this graph from log(x+1); so where was it originally?

Answer 26

Ummm i don't understand it. with the log... would it be x = -1, so that it could move to the right to get to 0?

Answer 27

thats absolutley correct :) they moved it over (+1) so it was originally at:

x=-1 .... any answers we get from looking at it from x=0 have to be "adjusted" now...by -1.

since the original Vasymp is at 0; the Vasymp has to be adjusted by (-1)..... Vasymp of log(x+1) is:

x=(0-1) or simply x=-1

Answer 28

OH! Okay!!!

Answer 29

That makes sense lol! Thank you!!

Answer 30

youre welcome :)