Find the rule and the graph of the function whose graph can be obtained by performing the translation 4 units right and 2 units up on the parent function

f(x)=|x|

Option B. is the correct option.

Step-by-step explanation:

In this question we have been given a function f(x) = |x|

When we perform a translation of 4 units right then the translated form of the function becomes f(x) = |x - 4|

And when we we translate the function up by 2 units then the transformed form is f(x) = |x - 4| + 2

Therefore the given graph in option B is the correct option.