Transformation: Reflection in the x-axis and vertical stretch by a factor of 2. Graph:
Practice makes perfect
We want to describe the transformations of the parent function f(x)=sqrt(x) represented by g(x)=- 2sqrt(x). 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 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)=- 2 sqrt(x)
We can describe the transformations as a reflection in the x-axis and a vertical stretch by a factor of 2. Let's make a table of values for f and g.
Parent Function
Transformation
x
sqrt(x)
f(x)=sqrt(x)
- 2sqrt(x)
g(x)=- 2sqrt(x)
0
sqrt(0)
0
- 2sqrt(0)
0
1
sqrt(1)
1
- 2sqrt(1)
- 2
2
sqrt(2)
sqrt(2)
- 2sqrt(2)
- 2sqrt(2)
4
sqrt(4)
2
- 2sqrt(4)
- 4
9
sqrt(9)
3
- 2sqrt(9)
- 6
Finally, we will plot the points for each function and connect them with smooth curves.
