Basically, a knowledge of even and odd functions can simplify certain calculations. One place where they frequently appear is when using trigonometric functions - for example, the sine function is odd, while the cosine function is even.
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You use an even function if f(-x) = f(x) for all x.You use an odd function if f(-x) = -f(x) for all x.
and you use neither if there is at least one point for which one or the other of the above is not true.
Most functions are neither even nor odd.
An even function is symmetric around the vertical axis. An odd function - such as the sine function - has a sort of symmetry too - around the point of origin. If you graph this specific function (for example, on the Wolfram Alpha website), you can see that the function has none of these symmetries. To prove that the function is NOT even, nor odd, just find a number for which f(x) is neither f(-x) nor -f(-x). Actually proving that a function IS even or odd (assuming it actually is) is more complicated, of course - you have to prove that it has the "even" or the "odd" property for EVERY value of x. Let f(x) = 2x3 - x2. Notice that f is defined for any x, since it is a polynomial function. If f(-x) = f(x), then f is even. If f(-x) = -f(x), then f is odd. f(-x) = 2(-x)3 - (-x)2 = -2x3 - x2 Since f(-x) ≠ f(x) = 2x3 - x2, f is not even. Since f(-x) ≠ - f(x) = -(2x3 - x2) = -2x3 + x2, f is not odd. Therefore f is neither even nor odd.
If f(x)=y, then the inverse function solves for y when x=f(y). You may have to restrict the domain for the inverse function to be a function. Use this concept when finding the inverse of hyperbolic functions.
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You turn of the Functions axes so you a completely clear graph screen. Then, you use the pt-change command to create your image. You can then use the StorePic command to store your image to Pic variable, which can be sent to a computer or recalled using the RecallPic command.
Chain Rule You can use the chain rule to find the derivative of the composite of two functions--the derivative of the "outside" function multiplied by the derivative of the "inside" function. The chain rule is related to the product rule and the quotient rule, which gives the derivative of the quotient of two functions.If you want example problems about the chain rule you should check out the related links!Hope this answers your question!