What differences do you see between the given function and the parent function? Apply those transformations to the graph of the parent function, y=sqrt(x).
Practice makes perfect
The given function is a cube root function.
f(x)= 2sqrt(x- 6)- 9
The graph of it will be a transformed version of the parent function, y=sqrt(x). Cube root functions typically follow the same general format.
f(x)= asqrt(x- h)+ k
To graph the given function, let's show the possible transformations of f(x)=sqrt(x).
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
Horizontal Translations
Translation right h units, h>0
y=f(x- h)
Translation left h units, h>0
y=f(x+ h)
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)
Using the table, we can graph the function as a series of transformations. Let's begin with the parent function.
Next, we will multiply the y-coordinates by a= 2. This stretches the graph of the parent function by a factor of 2.
Now, we will translate the graph 9 units down by subtracting 9 from each of the y-coordinates.
As our last transformation, we will translate the graph 6 units to the right. To do this, we will add 6 to each x-coordinate.
