logarithmic graphs

[umbral timber]

Hey guys I’m having trouble working this one out, would anyone be able to give me a hint?

[dense ledge]

Does it say
y = 1 - 2(log_e (x - 1))
?

If you are troubled with visualizing graphs I recommend you to use GeoGebra. It is free and can help a lot with vizualization, as you can freely adjust any variables and play around to see different results of your inputs.

[dense ledge]

Also, functions generally have a basic form that they follow.

You could start by sketching the graph of

y = ln(x) ------ (i)

Then notice, that

y = ln(x - a) -------- (ii)

moves (i) by a units to the right. Therefore,

y = ln(x-1)

moves (i) by one unit to the right.

Next, notice that

y = b × ln(x)

stretches graph (i) by a faktor of b and additionaly mirrors it over the x-axis if b is less than 0.
By the same logic, (ii) gets stretched. Now you can sketch the graph of

y = -2×ln(x-1).

For the final step note, that having a lone constant c (in your case 1) moves the entire graph up by c amounts of units (In your case by one unit).

Now you can sketch not only the graph of

y = -2×ln(x-1) + 1

but really any graph that follows the form

y = b × ln(x-a) + c

or, for that matter, any base really. With this step by step approach you do not need to limit yourself to base e logqrithms.

I hope that this was helpful.

@umbral timber

[umbral timber]

I used desmos and saw how the graph should look like

[mint pendant]

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