Question

How does the graph of f(x) = (x - 1)2 relate to the basic function f(x) = x??

a.
shift 1 unit to the left
shift 1 unit to the right
C.
d.
shift 1 unit up
shift 1 unit down
b.
Please select the best answer from the choices provided

Answer 1

It C

Explanation:

Answer 2

Shift 1 unit to the right, i.,e. option (c).

Explanation:

Note: Both functions can not be represented by f(x) and square is missing in basic function.

The given basic function is

`f(x)=x^2`

The given function is

`g(x)=(x-1)^2`

So, the given function can be written in the form of basic form as

`g(x)=f(x-1)` ...(1)

The translation is defined as

`g(x)=f(x+a)2+b` .... (2)

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

On comparing (1) and (2), we get

`a=-1,b=0`

Therefore, graph of f(x) shift 1 unit to the right to get graph of g(x).