Transformation: A horizontal translation left by 5 units, a vertical stretch by a factor of 2 and a vertical translation down by 4 units. Graph:
Practice makes perfect
We want to describe the transformations of the parent function f(x)=sqrt(x) represented by g(x)=2sqrt(x+5)-4. To do so, let's look at the possible transformations. Then we can more clearly identify the ones being applied.
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)
Vertical Stretch or Shrink
Vertical stretch, a>1
y= af(x)
Vertical shrink, 0< a< 1
y= af(x)
Vertical Translations
Translation up k units, k>0
y=f(x)+ k
Translation down k units, k>0
y=f(x)- k
Now, using the table, let's highlight the transformations.
g(x)= 2sqrt(x+ 5)- 4
We can describe the transformations as a horizontal translation left by 5 units, a vertical stretch by a factor of 2 and a vertical translation down by 4 units. Let's begin by graphing the parent function.
Next, we will multiply the y-coordinates by a= 2 This stretches the parent graph by a factor of 2.
Next, we will translate the graph 4 units down. To do so we will subtract 4 from every y− coordinate.
Next, we will translate the graph 5 units left.
Finally, let's show the graphs of f(x) and g(x) on the same coordinate plane.
