1. Sec. 2.5 Transformations of Functions

2. Vertical and Horizontal shifts
Transformations
Vertical and Horizontal shifts

3. Vertical and Horizontal shifts
h(x)=f(x)+c shifts graph up c units
h(x)=f(x)-c shifts graph down c units
h(x)=f(x-c) shifts graph to the right c units
h(x)=f(x+c) shifts graph to the left c units

4. Graph with your calculator f(x)=x2
This is a family of functions.
Notice the graph is the same size and shape but at a different location.
f(x)=x2+2
f(x)=x2-2
f(x)=(x-2)2
f(x)=(x+2)2

5. Mirror or flip the image
Reflections
Mirror or flip the image

6. Reflection in the coordinate axes
If y=f(x)
h(x)=-f(x) reflects in x-axis (flips over x-axis)
h(x)=f(-x) reflects in y-axis (flips over y-axis)

7. Use your calculator to graph f(x)=√x
Graph g (x) = -√x
It flips over the x axis
Graph h(x) = √-x
It flips over the y axis

8. Two types of transformations
Rigid- shape of graph is unchanged (Position changed)
Non-Rigid-distortion- changes shape of original graph

9. Vertical Stretch &Vertical Shrink
Caused by multiplying a function by a number

10. If c>1 in g(x)=c•f(x) then it is a stretch
If 0<c<1 (fraction) in g(x)=c•f(x) then it is a shrink

11. Graph f(x)=|x| Graph h(x)=3|x| This is vertical stretch
Graph g(x)=1/3|x|
This is vertical shrink

12. Horizontal stretch and shrink
A nonrigid transformation of y = f(x)
represented by h(x) = f(cx) where the
transformation is a horizontal shrink if c>1 and a horizontal stretch if 0<c<1.
Ex 5)