Question

Translations Y=|x+2|, Y=x^2+3, Y=|X-6|, Y=(X-4)^2, I need help to find the parent function, type of Translation domain, and range

Answer 1

Given the function

`Y=\mleft|x+2\mright|`

This function is a translation of the function (parent function):

`y=\mleft|x\mright|`

Because we have the following relationship between the two functions

`\begin{gathered} Y=y(x+2);\text{ } \\ \text{note: function notation, not product} \end{gathered}`

That is we move the x axis of the original function 2 units to the left

The domain of the function is any real number since it has no indeterminations, and the range is every positive real number since the function is an absolute value.