Embed Size (px)
Citation preview
• When we make a new function
based on an old one, we call it a
function transformation• Four basic categories:
• Translations (shifting)
• Dilations (shrinking or stretching)
• Rotations
• Reflections
We can use function notation to build new functions:
Example 1:
The outputs for k are the same as for f except we add 3 to them
Example 2:
The outputs for k are 2 times the outputs for f
( ) ( ) 3k x f x
( ) 2 ( )k x f x
Let f(x) be defined by:
Create the new function
x 0 1 2 3 4
f(x) 8 7 9 -2 5
x
k(x)
( ) ( ) 3k x f x
x 0 1 2 3 4
f(x) 8 7 9 -2 5
x
f(x) - 7
x
f(x)+10
Use f(x) to complete the tables below:
x 0 1 2 3 4
g(x) 12 9 -4 0 -1
x
g(x) – 3
Use g(x) to complete the table below:
Let f(x) be
defined by:
Graph the
new function:
( ) ( ) 2k x f x
Let f(x) be
defined by:
Graph the new
function:
( ) ( ) 1k x f x
Use the same f(x)
from the example:
Draw a graph for
the new function
Vertical shifts added/subtracted
something to the output values.
Horizontal shifts will add/subtract
something to the input values.
Example: h(x) = f(x + 1)
is a horizontal shift.
When the input is changed, we need to “undo” that change to see what happens to the graph/table.
So, f(x + 1) means we subtract 1from the x values.
And, f(x – 1) means we add 1 to thex values.
Output values stay the same!
Add/subtract (do the opposite!) to
change the input values.
Example:
Make a table for the new function
x 0 1 2 3 4
f(x) 8 7 9 -2 5
( ) ( 1)k x f x
x
k(x)
Make a table for the new function
x 0 1 2 3 4
f(x) 8 7 9 -2 5
x
g(x)
Remember we “undo” any change
to the input, so:
(x - #) means add shift right
(x + #) means subtract shift left
Here is f(x):
Sketch:
Here is f(x).
Sketch:
Dilations occur when a function is
multiplied by a number.
Vertical dilations – outputs multiplied
◦2f(x)
Horizontal dilations – inputs
multiplied
◦ f(2x) (We will only do vertical
stretches/shrinks this year.)
Make a table for the new function
x 0 1 2 3 4
f(x) 8 7 9 -2 5
x
g(x)
Make a table for the new function
x 0 1 2 3 4
f(x) 8 7 9 -2 5
x
h(x)
Here is f(x):
Sketch:
Here is f(x):
Sketch:
