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Even and odd functions
- Intro Lesson25:46
- Lesson: 15:14
- Lesson: 25:24
- Lesson: 36:31
- Lesson: 43:27
- Lesson: 59:21
Even and odd functions
If we are asked whether a given graph is symmetrical about the y-axis or not, it's easy to answer because we only need to see if there is a mirror image about the y-axis or not. But what if we are only given a function, but not the graph? In this section, we will broaden our knowledge about symmetry in functions while classifying symmetries algebraically, as well as learning the notion of odd and even functions.
Lessons
When f(−x)=f(x), function is even
f(−x)=−f(x), function is odd
f(−x)=−f(x), function is odd
- IntroductionWhat are even and odd functions?
• How to determine if it is an even or odd function graphically and algebraically? - 1.Determine if the function f(x)=7x9+12 is even, odd, or neither
- 2.Determine if the function f(x)=3x7+4x5−90x2 is even, odd, or neither
- 3.Determine if the function f(x)=400xsin(x) is even, odd, or neither
- 4.Determine if the function y=4x8+2x4−7x2 is even, odd, or neither
- 5.Determine if the function y=7csc(x)+2tanx is even, odd, or neither
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25.
Transformations
25.1
Transformations of functions: Horizontal translations
25.2
Transformations of functions: Vertical translations
25.3
Reflection across the y-axis: y=f(−x)
25.4
Reflection across the x-axis: y=−f(x)
25.5
Transformations of functions: Horizontal stretches
25.6
Transformations of functions: Vertical stretches
25.7
Combining transformations of functions
25.8
Even and odd functions