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C3 Help !!!

Can anyone please help me with this question ??

The function g is given by
g: x = ln |3x-6|, x Є R , x doesn't equal to 2.

(i) Sketch the graph of y = g(x).

(ii)Find the exact coordinates of all the points at which the graph of y = g(x) meets the coordinate axes.
Reply 1
Avatar for Pheylan
Pheylan
Draw the graph of y = ln(3x-6) and then do the modulus thing
Reply 2
Avatar for -__-'
-__-'
OP
Can you help me drawing it please?
whatever comes on the negative side, reflect it into the positive axis (above x-axis)
Reply 4
Avatar for andrew.P
andrew.P
Draw ln x, but times x coords by 1/3 and shift it 6 to the right. Then reflect in the y axis.
Reply 5
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-__-'
OP
okay, I understand the steps but still don't get the answer in the mark scheme. It is attached. Help please ?
untitled.bmp501.5KB
Reply 6
Avatar for -__-'
-__-'
OP
okay, i'll try to explain to you what is is confusing me.

I don't understand why is the point of intesrection with the x-axis is 7/3 rather than 19/3.
I got 19/3 by multiplying x= 1 by 1/3 and adding 6. Applying transformation.
I got x=1 from the fact that logarithmic function of the form y = ln (x) intesrescts with the x-axis at x = 1.

I also don't understand why is the graph reflected in the line x=2 rather than x=0 ( the y-axis)

Hope I delivered my points clearly.
Reply 7
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-__-'
OP
I see.
1 last question : why we didn't reflect it in the y-axis the way we do for graphs of the form y = f(|x|)?
Reply 8
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-__-'
OP
Thanks for helping ! It's soo kind of you !
I really do appreciate it.
:smile:

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