# Funky Functions

### By Tiana McCann

## Objective

In this lesson you will learn and understand how to use operations with functions. Below are examples and a video recap that will highlight the steps needs in order to successfully do operations on functions.

This can be found in the Accelerated Algebra 2 textbook, in chapter 6.1: Operations on Functions

## What is a Function?

A function can be represented by an equation such as f(x)=2x+1

## A Function This shows a function because for every x (represented by the orange oval) there is only one y (represented by the blue oval). | ## Function vs. Not This shows the difference between a function and not a function | ## Not a Function This does not show a function because for the letter "a" (representing a x value) has two values, 2 and 4. Since "a" has two answers that means this is not a function |

## A Function

## Operations on Functions

- Add
- Subtract
- Multiply
- Divide
- Composition

## Add Functions

**:**

__Equation__(f+g)(x) = f(x) + g(x)

__Steps:__

- Rewrite the functions f(x) and g(x) next to each other
- Add together the two functions
- (f+g)(x) is complete

__Tip:__ When adding the functions together, only add the numbers that have the same degree, such as you can add 7x + -x together but not 7x + -1 since the -1 does not have x.

## Subtract Functions

**:**

__Equation__(f-g)(x) = f(x) - g(x)

**Steps:**

- Rewrite the functions f(x) and g(x) next to each other
- Subtract the two functions together
- (f-g)(x) is complete

__Tip:__ When subtracting the functions together, only subtract the numbers that have the same degree, such as you can subtract -1 - 3 together but not 2x - 3 since the 3 does not have x.

## Multiply Functions

__Equation:__(fg)(x) = f(x) g(x)

**Steps:**

- Rewrite the functions f(x) and g(x) next to each other
- Multiply together the two functions by distributing each letter or number in the first parenthesis to the second parenthesis.
- Simply the multiplication of the two functions by either adding or subtracting the number and letter values together
- (fg)(x) is complete

__Tip:__ When multiplying the functions together, make sure to include all parts of the functions in fully multiplying through the two equations. Don't multiple similar values together such as (x+3)(x-2) = x^2-6, you have to multiply everything together such as (x+3)(x-2)= x^2-2x+3x-6. From there you would simplify by adding or subtracting similar degrees.

## Division Functions

**Equation:**f/g (x) = f(x)/g(x)

*g(x) cannot equal 0

__Steps:__

- Rewrite the function f(x) above g(x)
- Divide the two functions only if it can be or leave it as it is written
- (f/g)(x) is complete

## Composition Functions

__Equation:__f(g(x)) = (fog)(x)

__Steps:__

- Rewrite the functions in which g(x) is written inside of f(x) - the x in the f(x) function will have the g(x) function within it
- To simply f(g(x)) use arithmetic operations to get all the same degrees together
- f(g(x)) is complete

__Tip:__ When working on composition functions, make sure that all x values within f(x) have g(x) in them. For example: f(x) = x^2 + x and g(x) = x+5 which means f(g(x)) = (x+5)^2 +(x+5). From there follow factoring rules and arithmetic skills to gather all the same x's and number values together to reach the simplest form.

## Operations on Functions Recap

## Upcoming Assessments

**Quiz 4**:__Monday December 7th__**Test 2:**__Thursday December 10th__

## Citations

McGraw Hill Algebra 2 Textbook

https://www.mathsisfun.com/sets/function.html