Question

Consider the following function.

f(x) = √x - 2
Which of the following graphs corresponds to the given function?

Answer 1

The letter z is the correct answer

Answer 2

Graph Z

Explanation:

The radical parent function is

`g(x)=√(x)`

The given function is

`f(x)=√(x-2)`

`f(x)=g(x-2)` .... (1)

The translation is defined as

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

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

From (1) and (2) we get

`a=-2`

The value of a is negative so the graph of parent function shifts 2 units right.

Therefore, the graph Z represents the given function.