Unit 2 Lesson 3
The following graphs represent even and odd functions. I sorted the functions for you according to whether the function is an even function or an odd function. Even Functions
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Odd Functions
external image oddxxx.gif
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external image OddFunction.png?lang=en
In your virtual notebook answer the following questions:
Based on the classifications, when given a graphical representation what do you observe about all of the even functions?
Based on the classifications, when given a graphical representation what do you observe about all of the odd functions?
Do you think a function always has to be odd or even? Explain. Support your answer with an example if necessary.
How can you tell if a function is even or odd looking at a table of values? Explain.
How can you prove a function is even or odd algebraically? What steps should you take to prove whether a function is even of odd algebraically using the definition? Explain.
1. The graph is symmetrical about the y-axis.
2. The graph is symmetrical about the origin.
3. No, because not all graphs are symmetrical to either of the axis like an even and odd function.
4. If the y values are the same with same signs, then it's even. If the y-values are the same but with opposite signs, then it's an odd function.
5. For all x in the domain of f, f(-x) = f(x). This is when you plug in -x for all the in the function. Functions with this property are even.
For all x in the domain of f, f(-x) = -f(x). This means the entire function is negative and not just the x values. These functions are odd.
The following graphs represent even and odd functions. I sorted the functions for you according to whether the function is an even function or an odd function.
Even Functions
Odd Functions
In your virtual notebook answer the following questions:
1. The graph is symmetrical about the y-axis.
2. The graph is symmetrical about the origin.
3. No, because not all graphs are symmetrical to either of the axis like an even and odd function.
4. If the y values are the same with same signs, then it's even. If the y-values are the same but with opposite signs, then it's an odd function.
5. For all x in the domain of f, f(-x) = f(x). This is when you plug in -x for all the in the function. Functions with this property are even.
For all x in the domain of f, f(-x) = -f(x). This means the entire function is negative and not just the x values. These functions are odd.