Hello!
Left or right movement indicates a change in the x-value. As you can see, the graph of g(x) is 3 units to the left of f(x). To convey this in the function, you would add 3 to x; movement to the left is shown with addition and movement to the right is shown with subtraction.
Upward and downward movement indicate change in y-values. From the diagram it is evident that the graph moved down 2 units. To convey this, subtract 2 from y. Intuitively, subtraction means downward movement and addition means upward movement for y-values.
f(x) = x²
g(x) = (x + 3)² - 2
That's the answer! I hope this helps you.
