Question

identify a transformation of the function f(x) = √x by observing the equation of the function g(x) = √x-2

Answer 1

The transfomation made is a vertical translation 2 units downwards.

Explanation:

The parent function is

`f(x)=√(x)`

Remember that a parent function is the simplest function of its type, like this case the function
`f(x)` is the simplest form of radical functions.

The transformed function is

`g(x)=√(x)-2`

Notice that the difference between these two functions is that
`g(x)` has 2 units less on the vertical or dependent variable, such transformation indicates a vertical translation downwards.

Therefore, the transfomation made is a vertical translation 2 units downwards.

Answer 2

`f(x)=√(x)` is the Square Root Function. These are the characteristics of the graph of the square root function:

• The domain of the function is the set of all non negative real numbers.

• The range of the function is the set of all non negative real numbers.

• The graph has an intercept at
  `(0,0)`.

• The graph is increasing on the interval
  `(0, \infty)`.

Since the function
`g(x)=√(x)-2`, then this stands for the form:

`g(x)=f(x)-c`. This form tells us that the graph of f has been shifted c units downward where the value c = 2 in this problem. The graphs of both functions are shown below. The red one is
`f(x)` while the blue one is
`g(x)`