# Transformation in y=e^x

1. May 31, 2015

### Samurai44

1. The problem statement, all variables and given/known data
Describe the transformation in :
y=e6x-2 - 4
y=6ex-2 - 4 ?
2. Relevant equations
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3. The attempt at a solution
1)So 6x means stretch parallel to x-axis at s.f of 1/6
and then translation of ( +2 , -4 )
2) the same but the stretch is parallel to y-axis at s.f of 6

but which transformation comes first , and what's the difference if I switched them (in both cases)?

2. May 31, 2015

### Staff: Mentor

Did you plot the functions?
The -4 is fine, the +2 is not right.
You can make the description a bit easier if you use a rule for rewriting ea+b.

Right.

3. May 31, 2015

### Svein

4. May 31, 2015

### Samurai44

how +2 isnt correct ? ,,,its like f(x-2) which means translation of +2 in x direction ( to right )

5. May 31, 2015

### Samurai44

how do i know if the stretch is carried first or the translation ?
and whats the difference if it was the opposite

6. May 31, 2015

### Staff: Mentor

It is not. Subtracting 2 from x would mean $$e^{6(x-2)}-4$$That is not the same as your function.

Did you plot $e^{6x}-4$ and $e^{6x-2}-4$?

7. May 31, 2015

### SammyS

Staff Emeritus
There is no single "correct" sequence of transformations to get either of these. Changing the order of the transformations will often require the transformations themselves to be altered, but not always. There often is a "natural" order in which the tranfromations are performed -- this order suggested by the appearance of the function as it's presented to you.

For example 1) y=e6x-2 - 4

Yes. 6x means scaling parallel to the x-axis with a scale factor of 1/6, i.e. a shrink rather than a stretch.. That done first gives y = e6x.

Next you said translation of ( +2 , -4 ). I assume that refers to x, y respectively.
That's correct for the y, but for the x, that doesn't work.
It literally gives you y = e6(x-2) - 4.​
Try the translation first, then do the stretch/shrink. Otherwise, is there a different amount ti translate in the x direction?​

8. May 31, 2015

### Samurai44

The problem is these types of questions comes in multiple choice so i wont have enough time sketching or plotting.

I couldnt get the difference between e6(x-2) -4 and e6x-2 -4

9. May 31, 2015

### Staff: Mentor

6(x-2) = 6x-12 which is different from 6x-2.
You have enough time here and it helps to understand what went wrong, so you can get it right in the exam.

10. Jun 1, 2015

### Samurai44

so in case of 6(x-2) , the translation is +12 , but in 6x-2 , translation is +1/3 ?

11. Jun 1, 2015

### Staff: Mentor

For 6(x - 2), the translation is 2 to the right. For 6(x + 1/3), the translation is 1/3 to the left.

Compare the graphs of $y = e^x$ and $y = e^{6(x - 2)}$. The 6 in the 2nd version causes a compression of the graph of y = ex toward the y-axis by a factor of 6. If the multiplier happens to be smaller than 1, the transformation is an expansion away from the y-axis.
The x - 2 causes a translation of the compressed graph 2 units to the right.

You can see this by following a point on the graph of y = ex through both of these transformations

y = ex
Point (1, e) (or pick any point you like)

y = e6x
Point (1/6, e) -- Note that this point is 1/6 as far from the y-axis as (1, e) is. IOW, the point (1, e) has been "compressed" toward the y-axis.

y = e6(x - 2)
Point (13/6, e) -- Shift the point in the previous transformation two units right. 1/6 + 2 = 13/6.

If there are compressions/expansions and translations (shifts), you have to do the compressions/expansions before you do the translations. If you don't do them in this order, you don't get the right graph.