If the absolute value parent function has transformations applied such that it creates an absolute maximum at (-2,7). write an equation that could represent this new function?

The equation is y = -Ix + 2I + 7

Step-by-step explanation:

* Lets revise some transformation

- 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

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

 function g(x) = - f(x)

- The absolute value parent function is f(x) = IxI

- Its minimum value is (0 , 0)

- The minimum point changed from (0 , 0) to maximum point (-2 , 7)

- The minimum reversed to maximum, that means the parent function

  is reflected across the x-axis

- The x-coordinate changes from zero to -2 that means the parent

 function is translated to the left 2 units

- The y-coordinate changes from 0 to 7 that means the parent

  function is translated up 7 units

∵ f(x) = IxI

∵ f(x) is reflected across the x-axis

∴ g(x) ⇒ -IxI

∵ f(x) translated 2 units to the left

∴ g(x) ⇒ -Ix + 2I

∵ f(x) translated 7 units up

∴ g(x) = -Ix + 2I + 7

∵ g(x) = y

* The equation is y = -Ix + 2I + 7

Look to the attached figure for more understand