*If f(x)= f(-x) then the equation is an even function.*
*If f(-x)= -f(x) then the equation is an odd function.*
-If the power of x is even, then it is an even function because the negatives cancel out. For instance if the input of x is 1 or -1 for the equation y=x^2, then the output for y would still be 1.
Examples
f(x): x^2
f(x): absolute value of x
-Even functions are simply graphs that are symmetrical about the Y-axis whether it's the first and second quadrant or the third and fourth quadrant.
-If the power of x is odd, then it is an odd function because a negative is added. If the input of x is -1 for the equation y=x^3, then the output for y would be -1.
Examples
f(x)= x^3
f(x)= 1/x
-Odd functions are simply graphs that are symmetrical about the original. In other words, the graph has to be flipped horizontally and vertically to be symmetrical about the origin whether it's the first and third quadrant or the second and fourth quadrant.
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ReplyDeleteHow does the form f(x)=f(-x) give way to the negatives "canceling out"? What about the ones where there are no exponents, like cosine and sine?
ReplyDeleteI like this new take on the definition though.