write the transformation of X cubed if it is shifted right four units and then reflected over the X axis
x^3 -> (x-4)^3 -> -(x-4)^3
To find the transformation of the function f(x) = x^3 when it is shifted four units to the right and then reflected over the x-axis, you can follow these steps:
Step 1: Start with the original function f(x) = x^3.
Step 2: To shift the graph four units to the right, replace x with (x - 4) in the function. This moves all the points to the right by four units.
- The shifted function becomes g(x) = (x - 4)^3.
Step 3: To reflect the shifted graph over the x-axis, replace f(x) with -g(x) in the shifted function. This flips the graph upside down.
- The final transformed function is h(x) = -(x - 4)^3.
So, the transformation of f(x) = x^3 when shifted four units to the right and then reflected over the x-axis is h(x) = -(x - 4)^3.