sketching this log function (1 Viewer)

[JessGatz]

How would i go about sketching this...

Sketch y=log f(x)

when f(x) = 1 - ( x squared)

Can someone please talk me through the process...

 

[hyparzero]

y = ln (1 - x²)
=> y = ln[(1+x)(1-x)]
=> y = ln(1+x) + ln(1-x)
then sketch using watever appropriate method

 

[sasquatch]

How would i go about sketching this...

Sketch y=log f(x)

when f(x) = 1 - ( x squared)

Can someone please talk me through the process...

The best way to do i think would be to use the composite function method. First draw y = f(x) = 1 - x². then draw y = log f(x) taking values on the horizontal axis as f(x). What i mean here is to draw u = 1 - x², and draw y = log u, taking the horizontal-axis in terms of 'u' values, and not 'x' values.

From this you can see that say when x = 0, u = 1. and you know from your graph of y = log u, that when u = 1, y = log u = log 1 = 0. So the output of the graph y = log f(x), at x = 0, would be y = 0.

Do this for some other values to get the shape of the graph. Also you know that log u, is only defined for u > 0. so that means that from the graph of u = 1 - x², that y = f(x) is only defined for -1 <x < 1.

Get it?

 

[vafa]

this is 2 unit question not 4 unit.

 

[Nodice]

this is 2 unit question not 4 unit.

Be considerate of others who may not yet have the mathematical understanding that you have. This forum is made to help people, not to chastise others for their lack of knowledge, and your post was certainly not helpful.

Check the syllabus under graphs if you think this is not 4 unit, and not pertinent to this forum.
=)

 

[vafa]

ok, i am sorry if i have offended anyone but i was not going to...

here is the solution by 2unit knowlede
View attachment 13491