Transformation: Reflection in the x-axis and vertical translation down 1 unit. Graph:
Practice makes perfect
We want to describe the transformations of the parent function f(x)=sqrt(x) represented by g(x)=- sqrt(x)-1. To do so, let's look at the possible transformations. Then we can more clearly identify the ones being applied.
Transformations of f(x)
Vertical Translations
Translation up k units, k>0
y=f(x)+ k
Translation down k units, k>0
y=f(x)- k
Reflections
In the x-axis
y=- f(x)
In the y-axis
y=f(- x)
Now, using the table, let's highlight the transformations.
g(x)=- sqrt(x)- 1
We can describe the transformations as a reflection in the x-axis and a vertical translation down 1 unit. Let's consider the graph of the radical function f(x)=sqrt(x).
Next, we will apply the transformations to the graph of f(x) to obtain the graph of g(x).
