Question

Identify the transformations: y=2|x-4|

Answer 1

The original function is \[\Large y=\left| x \right| \]

Answer 2

Transformations change this original function, which we call the "parent function"

Answer 3

Hi welcome to Openstudy!

The "general" formula for the transformations of a function is this :
\(\LARGE y= \color{blue}{a}f(\color{red}{k}(x-\color{green}{d}))+\color{orange}{c}\)

where a is the vertical compression or stretch, and it also determines whether the function is reflected on the x-axis, "k" is the horizontal compression or stretch, and it also determines whether the function is reflected on the y-axis, "d" is the horizontal shift and "c" is the vertical shift.

the parent function of your equation is \(y=|x|\)

y=2|x-4| , as you can see you will have \(y= \color{blue}{a}|x- \color{green}{d}|=\color{blue}{2}|x- \color{green}{4}|\)

Answer 4

okay but would it be like... vertically stretched by 2, right 4??

Answer 5

yeah! absolutely right