- #1

- 306

- 5

- Homework Statement
- Sketch a graph, without the use of a calculator, y=log((x/(x+2))

- Relevant Equations
- y=log((x/(x+2))

I first attempted to find the x and y intercepts, algebraically, and discovered there were none. I then split the equation into y= log(x) - log(x+2) to see if that would give me any insight. It did not.

I used a graphing calculator and saw many similarities between x/(x+2) and log((x/(x+2)) but cannot make the leap to the latter.

I'm now considering the end behavior for the inner function and realizing there is a horizontal asymptote of y = 1. That means the end behavior of the outer function must have a horizontal asymptote at 0, since we are evaluating numbers closer and closer to 1 with the log function.

There is a vertical asymptote as x = -2

I think now I just need to test some points to see where the function is positive or negative.

And I just realized there must be an asymptote where the inner function is zero, i.e. x = 0. So I just tested some points and found the answer.

I used a graphing calculator and saw many similarities between x/(x+2) and log((x/(x+2)) but cannot make the leap to the latter.

I'm now considering the end behavior for the inner function and realizing there is a horizontal asymptote of y = 1. That means the end behavior of the outer function must have a horizontal asymptote at 0, since we are evaluating numbers closer and closer to 1 with the log function.

There is a vertical asymptote as x = -2

I think now I just need to test some points to see where the function is positive or negative.

And I just realized there must be an asymptote where the inner function is zero, i.e. x = 0. So I just tested some points and found the answer.

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