# Simple Transformation of a Function: translation, reflection, sketch

1. Jul 21, 2013

### kougou

1. The problem statement, all variables and given/known data

Hi all. I am having trouble to understand the combination of transformation on a function:

h(x)= a*f(b(x-c))+d

2. Relevant equations

The problem I am struggling with is the order of transformation; I do see that:
f(x-c) is translation in the right since every event happen before c in time;
f(bx) is the sketch if b is small <1, because it represents the same overall shape except that it has been skcetched.

What I am having trouble with is the order of transformation.

Say we have a function: f(-(x+4))
I do not understand why the transformation in above form (ie, combination of transformation), we should apply reflection first, then translation. Please don't tell me because it will give me the correct graph because I already know it will; what I am interested is the underlying principle.
Teacher told us we should apply "-", then translate "+4" to the left.

I see nothing wrong in applying translation first, then reflection; but obviously that will give me a wrong graph.

Thank you

3. The attempt at a solution

2. Jul 21, 2013

### kougou

ok. I see.

This question might be too simple for all \

or

you guys wouldn't even bother to explain such simple question?

3. Jul 21, 2013

### LCKurtz

Or maybe on a Sunday we are watching a golf tournament or something.

Here's a quote from the forum rules:

"Do not "bump" one of your threads to the top of a forum's thread list by posting a basically empty message to it, until at least 24 hours have passed since the latest post in the thread; and then do it only once per thread."

4. Jul 22, 2013

### Theorem.

What does f(-(x+4)) tell us to do with an input value? algebraically? The brackets tell us to apply the binary operation of addition and then multiply by 1. Each algebraic operation corresponds to a transformation here. Given a number ,say 2, what does -(2+4) tell you to do ? it doesnt tell you to multiply 2 by negative 1 and then add positve 4 ( -(2+4) does not equal (-2+4) ). What does this mean in the language of transformations? Remember that we are using the language of arithmetic to represent transformations.