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

Question

asked Sep 26, 2021 29.3k views

1 Answer

Vincent Koeman · Answer 1 · 2021-09-30T19:04:41+0000

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

y=f(x)

So:

Step 1. Reflection across the x-axis:

y=-f(x)

Step 2. Shifting 1 unit to the right

y=-f(x-1)

Step 3. Shifting 3 unit up

y=-f(x-1)+3

Finally:

g(x)=-f(x-1)+3

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.