Question

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

Answer 1

Explanation:

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.