Question

how did the equation shift from the parent function?y=f(x-4)the answer choices is A. vertical stretch by 4b. shift right by 4 C. Shift left by 4 D. Shift down by 4 E. horizontal stretch by 4

Answer 1

We can translate a function on its two axis. If we want to translate it on the vertical axis we need to add or subtract the constant that determines the translation by the end of the function, as seen below:

`f(x)+c`

If the constant is positive, then the function will be translated up, if its negative it'll be translated down.

We can also shift the function on its horizontal axis. To do that we have to add a constant in the argument of the function as seen below:

`f(x+c)`

If the constant is negative, the shift will happen on the right direction. If the constant is positve, the shift will be on the left direction.

The function given to us is:

`y=f(x-4)`

This falls on the second type of translation and the constant is negative, therefore there is a shift to the right by 4 units. The correct answer is b.