Why is the graph |loge(x)| reflected in the x-axis for all negative y values and loge|x| is reflecting the whole log graph in the y-axis?

Thanks

Asked Apr 10, 2014 by anonymous edited Apr 10, 2014 by Community

As you know, the modulus function makes negative things positive.

So when you put the whole function in the modulus function, the negative part of the graph becomes positive - hence |loge(x)| only reflects the negative y-values.

But when you put modulus around the x only (i.e. loge|x|), there are two steps involved: 1. First, think about |x| - if you had to list out the numbers it produced, it would look something like: 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5 2. Second, think about what you are doing when you say loge(x). You are plugging in -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 into loge(x). However, because you are saying loge|x|, the -5, -4, -3, -2, -1 are never plugged in in the first place. Instead, you are plugging in 5, 4, 3, 2, 1 (in place of -5, -4, -3, -2, -1). This is why the LHS of loge|x| looks like a reflection of the graph in the y-axis. It is because you are drawing the positive side (RHS) out twice.

Answered Apr 10, 2014 by Collin Li (56,060 points) selected Apr 10, 2014 by Community

## Modulus for logs - reflections

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