1. Section 1.7 Symmetry & Transformations
Chapter 1
Section 1.7
Symmetry & Transformations

2. Points and Symmetry

3. Types of Symmetry Symmetry with respect to the x-axis
(x, y) & (x, -y) are reflections across the x-axis
y-axis
(x, y) & (-x, y) are reflections across the y-axis
Origin
(x, y) & (-x, -y) are reflections across the origin

4. Even and Odd Functions Even Function: graph is symmetric to the y-axis
Odd Function: graph is symmetric to the origin
Note: Except for the function f(x) = 0, a function can not be both even and odd.

5. Algebraic Tests of Symmetry/Tests for Even & Odd Functions
f(x) = - f(x) symmetric to x-axis
neither even nor odd
(replace y with –y)
f(x) = f(-x) symmetric to y-axis
even function
(replace x with –x)
- f(x) = f(-x) symmetric to origin
odd function
(replace x with –x and y with –y)

6. Basic Functions

7. Basic Functions

8. Basic Functions

9. Basic Functions

10. Basic Functions

11. Basic Functions

12. Basic Functions

13. Transformations with the Squaring Function

14. Transformations with the Absolute Value Function

15. Transformation Rules Equation How to obtain the graph For (c > 0)
y = f(x) + c Shift graph y = f(x) up c units
y = f(x) - c Shift graph y = f(x) down c units
y = f(x – c) Shift graph y = f(x) right c units
y = f(x + c) Shift graph y = f(x) left c units

16. Multiply y-coordinates of y = f(x) by a
Transformation Rules
Equation How to obtain the graph
y = -f(x) (c > 0) Reflect graph y = f(x) over x-axis
y = f(-x) (c > 0) Reflect graph y = f(x) over y-axis
y = af(x) (a > 1) Stretch graph y = f(x) vertically by
factor of a
y = af(x) (0 < a < 1) Shrink graph y = f(x) vertically by
Multiply y-coordinates of y = f(x) by a