The function fx is a parabola The function gx is a transform

The function f(x) is a parabola. The function g(x) is a transformation of the function of the function f(x). The transformation that creates g(x) is f(x) moving 5 units to the lift and 2 units down. The function h(x) is a reflection of g(x) across the y-axis. a. White an equation that shows the relationship between f(x) and g(x). Show your work or explain how you know. b. Write an equation that shows the relationship between f(x) and h(x). Show your work or explain how you know.

Solution

a)

Shift to left by 5 units transforms f to f(x-5)

Shifting 2 units down gives

g(x)=f(x-5)-2

b)

Reflection across y axis sends x to -x for the same y

So,

h(x)=f(-x-5)-2