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How are functions different from relations that are not functions?
In mathematics the difference between a function and a relation is that each X-value in a function only has a single Y-value.
How are piece-wise functions different from other functions?
That means that the functions is made up of different functions - for example, one function for one interval, and another function for a different interval. Such a function is still a legal function - it meets all the requirements of the definition of a "function". However, in the general case, you can't write it as "y = (some expression)", using a single expression at the right.
What is the law of exponential functions?
There are several laws of exponential functions, not just one. Here is just one of them:The derivative of THE exponential function (base e) is the same as the function itself.
What does the single quote mean in functions?
For a function of only one variable it mean the derivative with respect to that variable. Thus, f'(x) = df(x)/dx. Occasionally, it can also refer to a variation of a function. For example, a family of functions, f(x), f'(x), f''(x) and so on.
How do graphs help you understand functions?
Typically, functions are graphed on x-y coordinates. A function of x means that for every x point, there must be a single y point. You can also many properties by graphing a function, such as the minimum and maximum points, slopes and inflection points, and the inverse of the function (y values plotted on x coordinate, and x values on y coordinate).
