Question

What is the function whose graph is the same as that of f(x) = -3x + 1 but shifted to the right 2 units and up 3 units?

Answer 1

Follow the general form for shifts f'(x) = m(x - h) + b + k, where the left/right shift is attached to the x and the up down shift is the k

In this case:
2 R (right is positive), and 3 up (up is also positive)

f'(x) = -3(x - 2) + 1 + 3
Simplify:
f'(x) = -3x + 6 + 1 + 3
f'(x) = -3x + 10