We want to use the given graph to write a rule for g. To do so, let's first identify the transformations that were applied to the parent function f(x)=sqrt(x).
We can see that the graph of g is a reflection in the y-axis followed by a horizontal translation right 2 units. Let's consider how these types of transformations affect the equation of the function.
Transformations of f(x)
Horizontal Translations
Translation right h units, h>0
y=f(x- h)
Translation left h units, h>0
y=f(x+ h)
Reflections
In the x-axis
y=- f(x)
In the y-axis
y=f(- x)
Using the table, we can write the transformations of f. Let's start by finding the rule for h, whose graph is a reflection in the y-axis of the graph of f.
h(x)=f(-x) ⇔ h(x)=sqrt(-x)
Finally, let's write the rule for g, whose graph is a translation right 2 units of the graph of h.
g(x)=h(x- 2) ⇔ g(x)=sqrt(- (x- 2))
We can simplify the above formula by using the Distributive Property.
