Which transformations are needed to transform the graph of y = f(x) to g(x) = -f(x - 1) + 3

Lets's solve this step by step. Here we have a function:

So:

Step 1. Reflection across the x-axis:

Step 2. Shifting 1 unit to the right

Step 3. Shifting 3 unit up

Finally:

So the graph of f has been reflected across the x-axis, shifted 1 unit to the right and 3 units up to become the graph of g.

associative property of multiplication