Transformation: Vertical shrink by a factor of 14 and a reflection in the y-axis. Graph:
Practice makes perfect
We want to describe the transformations of the parent function f(x)=x^(1/2) represented by g(x)= 14(- x)^(1/2). Let's start by rewriting f(x) and g(x) into the general format of a square root function.
f(x) = x^(1/2) &⇔ f(x) = sqrt(x) [0.5em]
g(x) = 1/4(- x)^(1/2) &⇔ g(x) = 1/4 sqrt(-x)
Now, let's look at the possible transformations. Then we can more clearly identify the ones being applied.
Transformations of f(x)
Vertical Stretch or Shrink
Vertical stretch, a>1
y= af(x)
Vertical shrink, 0< a< 1
y= af(x)
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)= 1/4 sqrt(- x)
We can describe the transformations as a vertical shrink by 14 and a reflection in the y-axis.
Let's begin by graphing the parent function.
Next, we will multiply the y-coordinates by a= 14. This shrinks the parent graph by a factor of 14.
Next, we will multiply the x-coordinates by -1. This reflects the graph across the y-axis.
Finally, let's show the graphs of f(x) and g(x) on the same coordinate plane.
