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
Function vs. Not
Not a Function
Operations on Functions
- Add
- Subtract
- Multiply
- Divide
- Composition
Add Functions
(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
(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
(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
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
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.htmlAccelerated Algebra 2
Email: tmccann@hillers.org
Location: Hopkinton High School
Phone: 555-555-5555