Question

What function translates the function f(x) = |x| to the right 2 units and up 10 units?

g(x) = |_| +__

Answer 1

Answer:
It is called a constant function :)
not sure if this is what ur looking for but I hope it helps!

Answer 2

`g(x)=|x-2|+10`

Explanation:

Translations

`f(x+a) \implies f(x) \: \textsf{translated $a$ units left}`

`f(x-a) \implies f(x) \: \textsf{translated $a$ units right}`

`f(x)+a \implies f(x) \: \textsf{translated $a$ units up}`

`f(x)-a \implies f(x) \: \textsf{translated $a$ units down}`

Given absolute value function:

`f(x)=|x|`

To translate the given function 2 units to the right, subtract 2 from the x-value:

`\implies f(x-2)=|x-2|`

Then to translate the given function 10 units up, add 10 to the function:

`\implies f(x-2)+10=|x-2|+10`

Therefore, the function that translates the function f(x) = |x| to the right 2 units and up 10 units is:

`\large\boxedx-2`