Question

If f(x) = x2, which of the following describes the graph of f(x - 1)?

The graph of f(x - 1) is a horizontal shift of f(x) = x2 one unit to the right.
The graph of f(x - 1) is a vertical shift of f(x) = x2 one unit down.
The graph of f(x - 1) is a vertical shift of f(x) = x2 one unit up.
The graph of f(x - 1) is a horizontal shift of f(x) = x2 one unit to the left.

Answer 1

The correct answer is:

The graph of f(x - 1) is a horizontal shift of f(x) = x^2 one unit to the right.

Explanation:

We are given a parent function f(x) as:

`f(x)=x^2`

Now we have to find what is the behavior of the graph of the transformed function:

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

Now we know that the transformation of the type:

`f(x+a)` with respect to the parent function f(x) is a shift either to the right or to the left i.e. a horizontal shift depending upon the sign of the constant 'a'.

If a>0 then the shift is to the left by 'a' units.

and if a<0 then the shift of he function is to the right by 'a' units.

Hence, here f(x-1) is a shift of the function f(x) to the right by '1' unit.