Question

Help please !! Given the parent function f(x) = x², define the function g(x) that

transforms f(x) as follows:


Reflection over the x-axis

Horizontal shift left 3 units

Vertical shift up 7 units

Answer 1

If f(x) = x^2

Then g(x) goes under the 3 transformations given...,

; Reflection on the x-axis...; -f(x)

; 3 units to the left...., -f(x + 3)

; 7 units up..., -f(x + 3) + 7

Then for....,g(x) = -f(x + 3) + 7

Where the function is going to be...

; g(x) = -(x + 3)^2 + 7

; g(x) = -(x^2 + 6x + 9) + 7

; g(x) = -x^2 - 6x - 9 + 7

;Hence the function of g(x) after all those transformations

g(x) = -x^2 - 6x - 2