[arvin_infinity]

It would be appreciated if someone help me out with sketching these 2 functions

1)

f(x)= e^-x+4 -2 ********* f(x)>=1

using transformation



2) f(x)= ln(4-2x) x<2
As for 2nd one I can sketch ln(-2x) but not ln (4-2x) !!!
To me its just ln(-2x) shifted by 4 units to the left on x direction but I am wrong according to the mark scheme!

+rep

[Llewellyn]

For these types of questions, sometimes it is helpful to re-write the function you are drawing.

For example: 1 could also be

And 2 could be ln(2(2-x)) and hence also ln(2-x) + ln2

In my opinion, those are much easier to work out in that form.

[notnek]

1)

Let

Can you draw ?

Then

You should know how to draw , given . Finally,




2)

Let then

Does this help?

You should never assume just by seeing e.g. an extra 4 in the function, that the function will be moved/stretched by 4 units. Always try to go through the steps like I've done above.

[arvin_infinity]

(Original post by notnek)
1)

Let

Can you draw ?

Then

You should know how to draw , given . Finally,




2)

Let then

Does this help?

You should never assume just by seeing e.g. an extra 4 in the function, that the function will be moved/stretched by 4 units. Always try to go through the steps like I've done above.

Well above confirms that my method was totally wrong but didn't really follow what you are doing...
why would you find h(x-2)?
am I reading it backwards ? as in you factorise the 2 and then you thought that's equal to h(x-2)?
Your method is totally new to me!

[arvin_infinity]

(Original post by Llewellyn)
For these types of questions, sometimes it is helpful to re-write the function you are drawing.

For example: 1 could also be

And 2 could be ln(2(2-x)) and hence also ln(2-x) + ln2

In my opinion, those are much easier to work out in that form.

Above did come into my mind but didn't know how to proceed further!

[Llewellyn]

(Original post by arvin_infinity)
Above did come into my mind but didn't know how to proceed further!

I would follow Notnek's advice here. It is better than what I proposed. What Notnek is suggesting is that you draw a familiar function, like e^-x and then you transform that.

This is generally not advisable, but if you have no idea how to tackle a question, I would recommend finding y when x= 0 and finding x(s) when y=0 and then finding the asymptotes and then drawing a general sketch. That isn't very good practice, but in an exam it would pick up quite a few marks.

[arvin_infinity]

(Original post by Llewellyn)
you draw a familiar function, like e^-x and then you transform that.

Yh pls elaborate a bit !!

[Llewellyn]

(Original post by arvin_infinity)
Yh pls elaborate a bit !!

Please excuse my rushed drawing. I also meant to say "4 units to the right" on my second diagram.

To get the x axis intercept, rearrange the equation to get x = 4- ln ((f(x) + 2) and set f(x) to 0.

Of course, the question asks you for x >= 1, in which case you will need to include this point (x, f(x)) when x =1.

Is there anything you don't understand?

[notnek]

(Original post by arvin_infinity)
Well above confirms that my method was totally wrong but didn't really follow what you are doing...
why would you find h(x-2)?
am I reading it backwards ? as in you factorise the 2 and then you thought that's equal to h(x-2)?
Your method is totally new to me!

I don't think the method is new to you but maybe you're out of practice or I went too fast. Here's a few more examples:



What is the transformation to get from f(x) -> g(x)?


A common mistake is to assume that the transformation will be by 2 units but this will not work e.g.




It makes things clearer if you factorise:



Now you should be able to see that so the transformation will be a translation 1 unit to the left.


Another example (similar to your question):

Factorising gives:




So f(x) -> g(x) is a translation 2 units to the right.

[arvin_infinity]

(Original post by Llewellyn)
x

You are a legend that drawing made it so clear for me..

(Original post by notnek)
x

Yh you both using the same method and I guess I was using a simplified stupid version of it in my head..cuz I would never write "am sketching f(x+2)" and therefore never occurred to me that am sketching something else
Lol at the common mistake..! I actually fell into that trap.

wondered if you guys have more practice questions on this