Functions

[rachelmaddie]

Can someone please check my work for this question?

Type of function: absolute value function
Given:
Parent function f(x) = |x|
Transformed function f(x) = 2| x + 3| - 5

Transformation 1: The function is multiplied by 2. Stretch vertically by a factor of 2
Transformation 2: The function inside the x value is added by 3. Translate left by 3 units.
Transformation 3: The function is subtracted by 5. Translate downwards by 5 units.

 

[lev888]

Transformation 2: The function inside the x value is added by 3.

The function inside x? I would phrase this differently.
Other than this, looks good.

 

[rachelmaddie]

The function inside x? I would phrase this differently.
Other than this, looks good.

How should I phrase it differently?

 

[lev888]

How should I phrase it differently?

It was f(x), now it's f(x+3). What did we do?

 

[rachelmaddie]

It was f(x), now it's f(x+3). What did we do?

Added the x value by 3?

 

[lev888]

Added the x value by 3?

Yes. Only increased, not added. Add to, increase by.

 

[yoscar04]

I would do first step 2, then step 1 and finally step 3.

 

[rachelmaddie]

Yes. Only increased, not added. Add to, increase by.

So how would I write that in a sentence?

 

[Dr.Peterson]

I prefer to say that "x is replaced with x+3"; that's what is being done to the function. To say that x is increased by 3 can lead to confusion with moving to the right.

I commonly list the horizontal transformations first, then the vertical, each in the right order within the group; but the order of horizontal relative to vertical doesn't matter. It's just a good habit.

 

[rachelmaddie]

I prefer to say that "x is replaced with x+3"; that's what is being done to the function. To say that x is increased by 3 can lead to confusion with moving to the right.

I commonly list the horizontal transformations first, then the vertical, each in the right order within the group; but the order of horizontal relative to vertical doesn't matter. It's just a good habit.

Transformation 2: The x value is replaced with x + 3. Translate left by 3 units.

Like that?

 

[yoscar04]

I would do first step 2, then step 2 and finally step 3.

Correction, 2, 1, 3.