To express h(x) in terms of x as a transformation of f(x), you need to identify the type of transformation applied to the original function f(x). In this case, f(x) is given as:
f(x) = (x + 2)³ - 3
The transformation can be broken down as follows:
The term "x + 2" indicates a horizontal shift to the left by 2 units.
The term "³" indicates a cubic function.
The term "-3" indicates a vertical shift downward by 3 units.
To obtain h(x), you can apply the same transformations to another variable, say k(x), and then express h(x) as a transformation of k(x). So, let's create k(x) first:
k(x) = x³ (This is the same cubic function as f(x) but without any shifts or translations.)
Now, apply the same transformations to k(x) to obtain h(x):
h(x) = k(x + 2) - 3
So, the expression for h(x) in terms of x is:
h(x) = (x + 2)³ - 3
This is the transformed function h(x) based on the given function f(x).