Question

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

Answer 1

Answer:

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

Step-by-step 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.