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