Question

Limits with graph. help.

Answer 1

For \(x < 3\), we have \(\dfrac{x-3}{|x-3|} = \dfrac{x-3}{-(x-3)} = -1\)

For \(x > 3\), we have \(\dfrac{x-3}{|x-3|} = \dfrac{x-3}{x-3} = +1\)

Now what?

Answer 2

since it's from the left hand limits, don't we only need when x is less than 3?

Answer 3

Very good. What do you conclude?

Answer 4

the limit is -1

Answer 5

That looks like it would be right for f(x). What about g(x)?

Answer 6

not sure but is it 2?

Answer 7

Take a good hard look at my first post. Why would it change by a factor of 2? The weird fraction either changes the sign or it doesn't. If f(x) is -1, then g(x) is +1 if it is left of x = 3.