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In mathematics there are many kinds of functions. Here is a short list of some of them: Polynomial functions: linear (ex. f(x) = 2x 1), quadratic (ex. f(x) = x 2 ), cubic (ex.
Here is a definition of a function. A function is a rule which maps a number to another unique number. In other words, if we start off with an input, and we apply the function, we get an output. For example, we might have a function that added 3 to any number. So if we apply this function to the number 2, we get the number 5.
We begin this discussion of functions with the basic de nitions needed to talk about functions. De nition 1. Let X and Y be sets. A function f from X to Y is an object that, for each element x 2 X, assigns an element y 2 Y . We use the notation f : X ! Y to denote a function as described.
(1) Identify the domain of a function, and evaluate a function from an equation. (2) Gain familiarity with piecewise functions. (3) Study the vertical line test.
Here are a few examples of functions. We will look at them in more detail during the lecture. Very important are polynomials, trigonometric functions, the exponential and logarithmic function. You won't nd the h-exponentials and h-logarithms in textbooks. But they will be important for us.
2 + 4 The minimum value of the expression is 0 + 4 = 4 and this minimum occurs when x = 1. So the function f (x) = (x 1) 2 + 4 will have a minimum at the point (1, 4). When x = 0, y = (0 1) 2 + 4 = 5. When x = 5, y = (5 1) 2 + 4 = 20. The range is 1 < f (x) < 20. 5 (1, 4) (5, 20) Domain Range x y O Exercise 1.2 1 Which of the mappings in E x e ...
One way of expressing a function is with an algebraic equation, such as. = px +1. This rule asserts that y equals the square root of whatever x is, plus 1. The variable x is called the independent variable or input of the function; y is called the dependent variable or output, because y depends on the value of x, which can be chosen independently.
