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

Answer:

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

Step-by-step 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:

$\large\boxed{g(x)=|x-2|+10}$