If you shift the quartic parent function, F (x) down 7 units and reflect it across the y-axis, what is equation of the new function?

The new function g (x) will be ⇒ g (x) = f (-x) ² - 7

Step-by-step explanation:

* Lets take about the transformation

- If the function f (x) reflected across the x-axis, then the new

function g (x) = - f (x)

- If the function f (x) reflected across the y-axis, then the new

function g (x) = f (-x)

- If the function f (x) translated horizontally to the right

by h units, then the new function g (x) = f (x - h)

- If the function f (x) translated horizontally to the left

by h units, then the new function g (x) = f (x + h)

- If the function f (x) translated vertically up

by k units, then the new function g (x) = f (x) + k

- If the function f (x) translated vertically down

by k units, then the new function g (x) = f (x) - k

* In the problem

- You will shift f (x) 7 units down and reflect it across the y-axis

- That means we will subtract f (x) by 7 and change x to - x

* The new function g (x) will be

g (x) = f (-x) - 7

* Look to the graph

- The red graph is f (x) = x²

- The blue graph is g (x) = (-x) ² - 7