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Chapter 1

- Section 1.7
- Symmetry Transformations

Points and Symmetry

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

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.

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)

Basic Functions

Basic Functions

Basic Functions

Basic Functions

Basic Functions

Basic Functions

Basic Functions

Transformations withthe Squaring Function

Transformations with theAbsolute Value Function

Transformation Rules

- Equation How to obtain the graph
- For (c gt 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

Transformation Rules

- Equation How to obtain the graph
- y -f(x) (c gt 0) Reflect graph y f(x) over

x-axis - y f(-x) (c gt 0) Reflect graph y f(x) over

y-axis - y af(x) (a gt 1) Stretch graph y f(x)

vertically by - factor

of a - y af(x) (0 lt a lt 1) Shrink graph y f(x)

vertically by - factor

of a - Multiply y-coordinates of y f(x) by a

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