Learning Objectives:

__Math Tutoring on The Properties of Functions__

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If we let f and **g** be **functions** and **x** is in the **domain** of both,

**1) (f + g )( x ) = f ( x ) + g ( x ) **

**2) (f - g )( x ) = f ( x ) - g ( x ) 3) ( f x g) ( x ) = f ( x) x g ( x ) **

**4) ( f/ g )( x ) = f ( x ) / g( x ) **

There are two main ways to determine if a **Function is Even or Odd. **One is an **algebraic method,** and the other is a **graphical method.**

A function is **Even** if **algebraically, f ( x ) = f ( -x )** and **graphically** the graph has **symmetry** across the **y axis.** A **polynomial function **will have all **even exponents **on the variables. For **odd** functions **algebraically, -f (x) = f ( -x)** and **graphically** the graph has **rotational symmetry**, about the **origin,** which means the graph remains the same after a rotation of **180 ^{0}**. A

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**Hook Questions:**

*1. **What are the basic properties of function?*

*2. **When is a function even?*

*3. **Define an odd function.*

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