Question

If the parent function is fx) = x^3 which transformed function is shown in the graph?

A. g(x) = (x-3)2
B. g(x) = (x+3)^3
C. g(x) = x^3 + 3
D. g(X) = x^3-3​

Answer 1

g(x) = (x-3)³ is the transformed function.

Explanation:

Horizontal shift:

If f(x) is the parent function.

Then horizontal shift can be expressed as:

, will shift left units.

`y = f(x - c)`, will shift
`f(x)` right c units.

Given the parent function

f(x) = x³

From the graph, it is clear that the transformed function is indicating that the parent function has been horizontally shifted right 3 units.

Therefore, according to the rule,
`y = f(x - c)`:

g(x) = (x-3)³ is the transformed function.

From the graph,

• The Red graph indicates the parent function i.e. f(x) = x³

• The Blue graph indicates the transformed function i.e. g(x) = (x-3)³

It is clear that the blue graph is obtained when the parent function has been horizontally shifted right 3 units.

Therefore, g(x) = (x-3)³ is the transformed function.