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C3 Log graph transformation

This is a question from one of the C3 Solomon papers:

How do I draw this graph? I'm guessing I start from the original graph of ln x, but in this there is the scale factor stretch of 3 parallel to the y-axis, the addition of 4 units 'up' and also the -ln(3x) which means a reflection in the x-axis. Which order would I apply these in?

Reply 1

KatsuoK

For y= 4 - ln(3x)

First of all, you would focus on all the things happening to your x variable.
The '3' in the (3x) means a stretch of scale factor 1/3 in the x-axis. The negative means a reflection in the x-axis.
Then I would focus on the things affecting the graph that correspond to the y-values, and would move the graph 4 units up.
If you're still having trouble, use Wolfram Alpha or google it, they usually have graphs, if you type in y = 4 - ln(3x), it should come up.

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Reply 2

davros

Original post by scientific222

This is a question from one of the C3 Solomon papers:

Personally I wouldn't even think about transformations when doing something like this - think about how the function behaves instead.

When x < 0, the logarithm isn't even defined, so there is nothing to plot for x < 0.

What happens near x = 0? This is probably going to be an asymptote.

What happens when x gets very big? The log gets big too so the overall function gets big and negative.

Work out where the function crosses the x axis - you can calculate this and mark it on the graph.

If you know the general shape of the ln function you can then use a similar shape for the required graph (in fact, note that ln(3x) = ln 3 + ln x, so your function is equivalent to (4 + ln3) - ln x)