Question

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

Answer 1

Answer:

The transfomation made is a vertical translation 2 units downwards.

Step-by-step explanation:

The parent function is

$f(x)=\sqrt{x}$

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

$g(x)=\sqrt{x}-2$

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

Answer:

$f(x)=\sqrt{x}$ 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 $g(x)=\sqrt{x}-2$, 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 $g(x)$