2. • When we make a new function based on an
old one, we call it a function
transformation
• Come in four basic categories:
• Translations (shifting/sliding)
• Dilations (shrinking or stretching)
• Rotations
• Reflections
• For now, we will study only
translations and dilations.
3. We
can use function notation to build
new functions:
f ( x) 3
Example 1: k ( x)
The outputs for k are the same as for f
except we add 3 to them
2: k ( x) 2 f ( x)
The outputs for k are 2 times the
outputs for f
Example
4.
Here’s the definition of f(x):
x
f(x)
0
8
1
7
2
9
3
-2
4
5
I want to make a new function k ( x)
What does the table look like?
x
k(x)
0
11
1
10
2
12
3
1
4
8
f ( x) 3
5. Use
this function definition to complete
the definitions below:
x
f(x)
0
8
1
7
2
9
3
-2
4
5
x
f(x)-7
0
1
2
3
4
x
f(x)+10
0
1
2
3
4
6. Use
this function definition to complete
the definition below:
x
g(x)
x
g(x) – 3
0
12
1
9
2
-4
0
1
2
3
0
3
4
-1
4
7. Here’s
the
definition of f(x):
I
want to make a
new function
k ( x) f ( x) 2
What does the
graph look like?
10. 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.
11. 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 1
from the x values.
And, f(x – 1) means we add 1 to the x
values.
12. Output values stay the same!
Add/subtract (do the opposite!) to change
the input values.
x
0
1
2
3
4
Example:
f(x)
8
7
9
Make a table for the new function
k ( x)
x
k(x)
f ( x 1)
-2
5
17. 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.)
