function question

Question

How can you tell if a function has been translate vertically versus horizontally?

How can you tell if a function has been translate vertically stretched versus horizontally stretched?

How can you tell if a function has been translate vertically compressed versus horizontally compressed?

Answer 1

Linette,

 

I wish I has answered this question before the first one I answered.

 

Here are the explanations:

 

Say, f(x) is the function you would like to transform.

 

Then y = f(x) + k will be translated vertically |k| units (up is k > 0 and down if k < 0),

 

y = f(x - h) will be translated horizontally |h| units (right is k > 0 and left if k < 0).

 

You can tell which is occurring by looking at the function and seeing where the modification occurs, added/subtracted from the function, or added/subtracted from x inside the function.

 

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The function y = a f(x) will be stretched vertically if a > 1.  (If 0 < a < 1, it will be compressed vertically.)

 

The function y = f(a x) will be stretched horizontally if 0 < a < 1. (If , it will be compressed horizontally.)

 

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Your last question was answered in the parenthetical remarks in the last explanation.

 

I know this is all a bit abstract. Fell free to reply back if anything requires more explanation or examples are needed. You did ask an abstract question, so this will be the best I can do for you right now without specific examples related to what you are trying to understand.