Respuesta :

danielmaduroh

Answer:

[tex]f(x)=\sqrt{x}[/tex] 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 [tex](0,0)[/tex].
  • The graph is increasing on the interval [tex](0, \infty)[/tex].

Since the function [tex]g(x)=\sqrt{x}-2[/tex], then this stands for the form:

[tex]g(x)=f(x)-c[/tex]. 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 [tex]f(x)[/tex] while the blue one is [tex]g(x)[/tex]

Ver imagen danielmaduroh

Answer:

The transfomation made is a vertical translation 2 units downwards.

Step-by-step explanation:

The parent function is

[tex]f(x)=\sqrt{x}[/tex]

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

The transformed function is

[tex]g(x)=\sqrt{x}-2[/tex]

Notice that the difference between these two functions is that [tex]g(x)[/tex] 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.

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