Question

Given the parent function of f(x) = x3, what change will occur when the function is changed to f(x − 3)?

Shift to the right 3 units
Shift to the left 3 units
Shift up 3 units
Shift down 3 units

Answer 1

Answer:

Shift to the right 3 units.

Answer 2

Answer:

Shift to the right 3 units

Step-by-step explanation:

Translations are a type of rigid transformation of functions, in which the position of the graph of a function is modified. The general form of the graph of a function moves up, down, left, or right.

Vertical translations:

Let:

$a >0$

$y=f(x)+a$  shifts the graph $a$ units up

$y=f(x)-a$ shifts the graph $a$ units down

Horizontal translations:

Let:

$b>0$

$y=f(x+a)$ shifts the graph $b$ units to the left.

$y=f(x-a)$ shifts the graph $b$ units to the right.

Using the previous information we can conclude that the function:

$f(x-3)$

Is a Horizontal translation in which the graph was shifted $b=3$ units to the right.

$f(x-3)=(x-3)^3$

I leave you the graphs, so you can corroborate the answer easily.