Example 1: easy
f(x)=√(x-2) +3
First let's make a list of the transformations we will perform.
1. Right 2
2. Up 3
Now apply the transformations to your basic points.
(0,0) -> (2,3)
(1,1)-> (3,4)
(4,2)-> (6,5)
Graph.
First let's make a list of the transformations we will perform.
1. Right 2
2. Up 3
Now apply the transformations to your basic points.
(0,0) -> (2,3)
(1,1)-> (3,4)
(4,2)-> (6,5)
Graph.
Example 2: Medium
f(x)=-2√1/2(x+4) -1
1. Reflection over x axis
2. Vertical stretch by factor of 2
3. Horizontal stretch by factor of 2
4. Left 4
5. Down 1
(0,0)-> (-4,-1)
(1,1)-> (-2, -3)
(4,2)-> (4, -5)
1. Reflection over x axis
2. Vertical stretch by factor of 2
3. Horizontal stretch by factor of 2
4. Left 4
5. Down 1
(0,0)-> (-4,-1)
(1,1)-> (-2, -3)
(4,2)-> (4, -5)
Example 3: Hard
Try one on your own!
f(x)=-1/3√-4(x-7) +7
f(x)=-1/3√-4(x-7) +7
Example 4: Real Life Application
An airplane manufacturer determine the size of an airplane wing according to the function f(x)=√(x) and the equation y=0. A new wing design calls for the use of the new function g(x)=1/2√3(x+1).
a. Describe the new function as a transformation of the original function.
b. Graph the original and the transformed equations.
a. Describe the new function as a transformation of the original function.
b. Graph the original and the transformed equations.