EVEN FUNCTION
The formula for an even function is defined as f(-x)=f(x) for a function of y=f(x). Graphically an even 
function would be symmetric about the y- axis as seen in the image.
function would be symmetric about the y- axis as seen in the image.Since y=f(x) and according to the formula for an even function f(-x)=f(x) then for an even function y=f(-x). For an even function it does not matter whether the input for x is negative or positive because the outcome (y) be the same, which is why there is symmetry about the y-axis. As seen in the example for an even function f(x)=x^2 the input can be negative or positive but the outcome will be the same. f(2)=2^2=4 , f(-2)=(-2)^2=4.
ODD FUNCTION
The formula for an odd function is f(-x)=-f(x) for a function of y=f(x). An Odd function if graphed will have symmetry about the origin as seen in the image. The formula basically says that if a negative value is imputed into a function the outcome(y) will be the negative value of the function for a positive value f(-x)=-y. For example in the odd function f(x)=x^3 if -2 is imputed the result would be f(-2)=(-2)^3, which is f(-2)=-8.
If a positive value is imputed the outcome will be positive. From the formula we can see this
f(-x)=-f(x)in seeing what the value for a positive number would be -f(-x)=f(x),-(-y)=f(x), y=f(x).
For example in the odd function f(x)=x^3 if two is imputed the value would be f(2)=2^3,
f(2)=8
Great explanation for the even! However, your odd explanation has some holes. The graph of y=-x^3 is also odd but it doesnt meet your explanation. If a positive number is put in, a negative output comes out, etc.
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