Write a rule for g (x) =

Question

Let the graph of g be a vertical stretch by a factor of 3 and a reflection in the y-axis, followed by a translation 2 units left of the graph of f (x) = x^2-4x+1. Write a role for g.

Answer 1

f(x) = (x - 2)² - 3 by completion of the square

g(x) = 3(x - 2)² - 3 stretch by 3

g(x) = -3(x - 2)² - 3 reflect over y-axis

g(x) = -3(x - 4)² - 3 shift 2 to the left (same as 2 to the right in original