Question

Let the graph of g be a translation 2 units up and 2 units right, followed by a reflection in the y-axis of the graph of f(x) = -(x + 3)2. Write a rule for g.

Answer 1

g(x) = 2x

Explanation:

translation 2 units up:

g(x) = -(x+3)*2+2

shift 2 units right:

replace each x with x-2

g(x) = -((x-2)+3)*2+2

g(x) = -(x+1)*2 + 2

g(x) = -2x-2+2

g(x) = -2x

reflect across the y-axis:

change sign of slope

g(x) = 2x