Even, Odd, or Neither Functions The Easy Way! - Graphs & Algebraically, Properties & Symmetry

This algebra 2 and precalculus video tutorial explains how to determine whether a function f is even, odd, or neither algebraically and using graphs. This video contains plenty of examples and practice problems using variables and constants. First, plug in -x into the equation and see if the sign changes. If all signs change, it's an odd function. If they all remain the same, then it's an even function. If some change while others do not, the function is neither even or odd. For graphs, even functions are symmetric about the y axis. For odd functions, the symmetry exists about the origin. For circles with even and odd properties, it does not pass the vertical line test and is therefore not a function.
Introduction to Functions:
• Functions - Vertical L...
Evaluating Functions:
• Evaluating Functions -...
Function Operations:
• Function Operations
Increasing and Decreasing Functions:
• Increasing and Decreas...
Relative Maximum & Minimum Values:
• Identifying The Relati...
_____________________________________
Relations and Functions:
• Relations and Function...
Domain and Range From a Graph:
• Domain and Range of a ...
How To Find The Domain of a Function:
• How To Find The Domain...
Average Rate of Change of a Function:
• Average Rate of Change...
The Difference Quotient of a Function:
• Difference Quotient
_____________________________________
Evaluating Piecewise Functions:
• Evaluating Piecewise F...
Graphing Piecewise Functions:
• Graphing Piecewise Fun...
Composite Functions:
• Composite Functions
How To Evaluate Composite Functions:
• How To Evaluate Compos...
Composite Functions - Data Table:
• How To Evaluate Compos...
Comp. of 3 Functions - Data Table:
• Composition of Three F...
Decomposing Functions:
• Decomposing Functions ...
_________________________________
Introduction to Inverse Functions:
• Introduction to Invers...
How To Find The Inverse of a Function:
• How To Find The Invers...
Verifying Inverse Functions:
• Verifying Inverse Func...
Horizontal Line Test - 1 to 1 Functions:
• Horizontal Line Test a...
Vertical Line Test:
• Vertical Line Test
Graphing Inverse Functions:
• Graphing Inverse Funct...
Composite and Inverse Functions:
• Composite Functions an...
__________________________________
Even and Odd Functions:
• Even, Odd, or Neither ...
Transformations of Functions:
• Transformations of Fun...
Linear Functions:
• Linear Functions
Functions and Graphs - Problems:
• Functions and Graphs |...
Functions - Test Review:
• Functions
______________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/
Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
Functions and Graphs: ruclips.net/video/ZTEv8OnGaxo/видео.html
Transformations of Functions: ruclips.net/video/tyQLp6x-GoU/видео.html
Graphing Polynomial Functions: ruclips.net/video/rOOefdqMvtA/видео.html
Next Video: ruclips.net/video/BtcKotD6Ni8/видео.html

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I needed this refresher. This stuff might seem unimportant now, but it gets important once you get to calculus 2. You will eventually be given an impossible-to-solve problem that simplifies to 0 but only if you know if the function is even.

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[@Rainsong777]

Just after 08:08, you left out the minus in front of the f(x) that proves the function is ODD...
f(-x) = -f(x)
Amazing & clear explanations......... Thank you......!!!!!!!!!

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P.S. You missed a negative sign at 8:10

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All these years trying to fully understand the odd function notation f(-x)=-f(x), and now with the factoring out the "-1" finally and suddenly it all made sense! I know I'm late to the party, but thanks anyways...🤣😂😀

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[@xogmaster]

8:12 on the bottom it should say f(-x) = -f(x) for odd function

[@jeromeporter9613]

should that actually say f(x) = -f(x)? I promise I'm not trying to call you out. I got super confused and I'm trying to understand why it should be f(x) = -f(x).

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probably a mistake

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You've explained how to determine whether a function is even or odd very well and clearly
Thank you

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6:04 "Anything raised to the 0 power is one"
Me: Raises 0 to the power of 0 and obtains 1
Maths: You are a joke to me!

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Indeterminate form.....

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And also by the way, in 13:18 this isn't a function right? So it means that the answer isn't 'neither'?

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