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

Shift to the right 3 units.

Answer 2

Shift to the right 3 units

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.