Determine the relationship between the functions f(x) and g(x):
1. $f(x)=|x| ; g(x)=|x|+6

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Answer

So, the graph of g(x) would be the graph of f(x) shifted upwards by 6 units.

Steps

Step 1 ：The functions f(x) and g(x) are related in such a way that g(x) is a vertical translation of f(x) by 6 units upwards.

Step 2 ：This is because g(x) = f(x) + 6, which means that for every x, g(x) is always 6 units greater than f(x).

Step 3 ：So, the graph of g(x) would be the graph of f(x) shifted upwards by 6 units.