1. TRANSFORMATIONS OF FUNCTIONS
Honors Precalculus
January 31, 2018
Mr. Agnew

2. Essential Question Essential Vocabulary
How do we transform the graphs of functions?
Essential Vocabulary
Transformation
Reflection
Shift
Parent Function

3. Reflecting Functions
The parent function can be reflected over the x or y axis.
Reflect over x axis: y = - f(x)
Reflect over y axis: y = f(-x)

4. Vertical Shifts
A number added to the entire function shifts the graph up & down.
Shift c units up: y = f(x) + c
Shift c units down: y = f(x) – c

5. Horizontal Shifts
A number added to the x variable shifts the graph left and right.
Shift c units left: y = f(x + c)
Shift c units right: y = f(x – c)
Examples

6. Stretching & Shrinking
Stretch vertically by factor of a
y = af(x), |a| > 1
Shrink vertically by factor of a
y = af(x), 0 < |a| < 1
***Multiply all y coordinates by a.

7. Stretching & Shrinking
Shrink horizontally by factor of 1/a y = f(ax), |a| > 1 Stretch horizontally by factor of 1/a y = f(ax), 0 < |a| < 1 ***Multiply all x coordinates by 1/a
Examples

8. Homework
Worksheet Provided