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

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