1 Let gx x2 Find a formula for a function gx whose graph is

1. Let g(x) = x² Find a formula for a function g(x) whose graph is obtained from the following sequence of transformations. No graphing is needed.

(a) Reflect across the x-axis

(b) Shift right 2 units

(c) Shift left 2 units

Solution

g(x)=x²

(a) Reflect across the x-axis

g(x)=- x²

(b) Shift right 2 units

g(x)=- (x-2)²

(c) Shift left 2 units

g(x)=- (x-2+2)²

g(x)=- x²