Final answer:
The function rule for g(x) that is a translation of f(x) = |x| up 5 units is g(x) = |x| + 5. This moves the graph of f(x) up by 5 units on the y-axis, maintaining its V-shape with the vertex shifting from (0,0) to (0,5).
Step-by-step explanation:
To perform a translation of the function f(x) = |x| up by 5 units, you need to add 5 to the function's value. Therefore, the new function g(x) will be g(x) = |x| + 5. This effectively shifts the entire graph of f(x) upwards by 5 units on the y-axis without changing the shape or orientation of the graph.
The original function f(x) is the absolute value function which takes the positive value of x regardless of whether x is positive or negative, hence its V-shaped graph. When we translate this graph upwards, every point on the graph moves straight up by 5 units, meaning that the V-shape is maintained.
It's essential to understand that the translation does not affect the x-values or the width of the graph, just the y-values. Therefore, after the translation, the vertex of the V, which was originally at the origin (0,0), will now be at (0,5).