In which direction must the graph of f (x) = 7x be shifted to produce the graph of g (x) = 7x - 3?

"the graph of f (x) needs to be shifted vertically 3 units down to produce the graph of g (x) "

Step-by-step explanation:

If we have a function of the form:

f (x) = ax

We can say:

f (x) = ax + b is the parent shifted b units up f (x) = ax - b is the parent shifted b units down f (x) = a (x-b) is the parent shifted b units right f (x) = a (x+b) is the parent shifted b units left

These are the function transformation rules (both vertical and horizontal shift).

Looking at the transformed function, g (x) = 7x - 3, this goes with the rule "transformation vertically 3 units down" from the rules above.

So the graph of f (x) needs to be shifted vertically 3 units down to produce the graph of g (x).