Let f ( x ) = 4 √ x If g ( x ) is the graph of f ( x ) shifted down 6 units and right 2 units, write a formula for g ( x ) g ( x ) =

Question

Let If  is the graph of  shifted down 6 units and right 2 units, write a formula for = 

Answer 1

f(x) = 4√x 

g(x) = 4√(x - 2) - 6 

g(x) * g(x) = [4√(x - 2) - 6] * [4√(x - 2) - 6]

g(x) * g(x) = [4√(x - 2) - 6]²  => using (a - b)² = a² - 2ab + b²:

g(x) * g(x) = [4√(x - 2)]²  - [2 * 6 * 4√(x - 2)] + 6²

g(x) * g(x) = 16(x - 2) - 48√(x - 2) + 36

g(x) * g(x) = 16x - 32 - 48√(x - 2) + 36

g(x) * g(x) = 16x + 4 - 48√(x - 2)

Or in factored form:

g(x) * g(x) = 4[4x + 1 - 12√(x - 2)]