Question

The graph of y=h(x) is a transformation of the graph of y=f(x)

Given that f(x) = (x + 2)³-3, write an expression for h(x) in terms
of x.

Answer 1

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).