Even functions
whatever the input is, whether its positive or negative, if the output comes out positive then the function is even, but if it comes out negative its an odd function. For example in the function of f(-x)= x^2, if you plug in a negative number such as -1, it comes out positive, f(-1)=(-1)^2 , f(-1) = 1 , if one were to graph it, it would be symmetrical about the y axis, the only number that would change would be the x, if it was 2 in the x axis in quadrant 1, then in quadrant 2 the x would be -2, but the y would be the same for both quadrants. In other words, what ever the input is, if the output is positive, then the function is even and symmetrical to the y-axis.
odd function
an example of a odd function would be f(-x)=x^3. If x were to be -1 like this, f(-1)= (-1)^3, it would equal f(-1)= -1, it would be negative. In this case, it would be symmetrical about the origin meaning that it would look the same if one of the sides was flipped either upside down or right way up. But since it is not symmetrical about the y-axis, it is symmetrical about the origin, across from each other, like in the graph, one side is in quadrant one while the other is in quadrant three. In other words, what ever the input is, if it comes out negative, then the function is odd and is symmetrical about the origin.
ha ha yours was really thorough and detailed
ReplyDeletei dont think that everytime the output comes out negative it means it is an odd function.
ReplyDeletebut i still understand what you are trying to say..
like the odd function is supposed to be symmetrical in a "diagonal" way (or about the origin).
"whatever the input is, whether its positive or negative, if the output comes out positive then the function is even, but if it comes out negative its an odd function."
ReplyDeleteI love how you explained the first half about positive and negative inputs! =) BUT, y=-x^2 is also even, even if the outputs come out negative...
"it would look the same if one of the sides was flipped either upside down or right way up."
Even your example of flipping the x^3 does not follow your statement. Be careful of what you are saying.