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