Question

Find the domain and the equation of the vertical asymptote for the function f(x) = log(3 - x)

Answer 1

Vertical asymptote is when x is not equal to 0

Answer 2

@Loser66 @Hero

Answer 3

Have you tried graphing log(3 - x)?

Answer 4

I did on my calculator. I set x - 3 > 0 for domain and x -3 = 0, the way it is written is log(3 - x) but I think it is easier to change it to log(x-3)

Answer 5

Domain: x > 3 (but the answer is -oo, 3), and I don't see why -oo would be included in the domain
V.A. x = 3

Answer 6

@Hero, I was thinking that log is positive values so it wouldn't include negative infinity

Answer 7

The domain of log( ) occurs when the argument of log( ) is greater than zero. In this case the argument of log( ) is 3 - x, therefore 3 - x > 0.

Answer 8

Oh so I can't just change it to x - 3 because I thought 3 -x and x -3 were the same thing according to wolfram alpha when I wanted to see if they could be switched around

Answer 9

\(3 - x \ne x - 3\)

Example: let x = 2

\(3 - 2 = 2 - 3\)
\(1 = -1\)
False

Answer 10

|3 - x| = |x - 3|

Answer 11

That is because of absolute value

Answer 12

That's the only way they become equal.

Answer 13

So to find the domain, I am setting 3 -x > 0 and 3 -x = 0 to find the vertical asymptote.

Answer 14

Yes, that appears to be correct.

Answer 15

3 - x > 0
Subtract 3 from both sides
-x > -3

Answer 16

No, I wouldn't approach it that way.

3 - x > 0

Add x to both sides:

3 > x

Answer 17

Oh I would have got into some trouble had I solved it that way... that is where I need help is in my approaches to problems

Answer 18

Ok, so I get 3 > x for the domain and 3 = x for the equation of the asymptote

Answer 19

Actually, x = 3 is the equation

Answer 20

You can solve it your way as well. I just do it the way I do because I avoid negatives at all costs.

Answer 21

Because if you have negatives you end up having to flip signs and in my mind, flipping a sign is not a valid mathematical step.

Answer 22

That is a good rule to follow. The domain would be (-oo, 0) U (0, 3)

Answer 23

The domain is (-oo, 3)

Answer 24

Why is it -oo? Is that because a logarithm has a domain of -oo, oo?

Answer 25

We said that the domain is 3 > x

Answer 26

Yes and 3 > x is equivalent to x < 3

Answer 27

Did you not learn this when you were little?

Answer 28

Oh I was thinking of 3 > x as the same as x > 3

Answer 29

Try not to get mixed up with that

Answer 30

No, I get confused on this concept of switching signs

Answer 31

Whether you have 3 > x or x < 3, the pointy end is always facing x and bigger end is always facing 3.

Answer 32

That's how you keep up with things without confusing them.

Answer 33

I'm sure I heard that when I was little but I forgot it.

Answer 34

I'm going to put that in my notes.