The set of permissible outputsĪ function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. The set used to define a function is called the domain of the function. With this self-paced course, you get engaging. The input and output of a function could be real numbers, the integers, a subset of the rational numbers, a set of real numbers, or more general objects such as vectors. Physics 101 has been evaluated and recommended for 3 semester hours by ACE and NCCRS and may be transferred to over 2,000 colleges and universities. A function could be described implicitly, for example as the inverse to another function or as a solution of a differential equation, or it could be described explicitly, as a formula or as a graph. In science, functions are sometimes defined by a table that gives the outputs for selected inputs. Others are given by a picture, called the graph of the function. Some functions may be defined by a formula or algorithm that tells how to compute the output for a given input. There are many ways to describe or represent a function. The output of a function f corresponding to an input x is denoted by f(x), which is read as "f of x" or "f at x", or simply "f of x", when the context makes it clear.įunctions of various kinds appear in many areas of mathematics, and their study is one of the central topics of modern mathematics. An example is the function that relates each real number x to its square. The notion of a function is one of the most fundamental concepts in mathematics. The exponential function is also used to model exponential growth, in which a constant change in time gives the same proportional change in some other quantity.Ī function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Its slope is positive, since ex has a positive slope. The graph of y = ex is upward-sloping, and increases faster as x gets larger. ![]() The exponential function is also used to model exponential growth, in which a constant change in time gives the same proportional change in some other quantity. The graph of y = ex is upward-sloping, and increases faster as x gets larger. For answers to your questions about the course use the links below: Instructor Course Catalog Description Course Description. ![]() The exponential function is used to model a relationship in which a constant change in the independent variable gives the same change in the dependent variable. The exponential function is a special case of the hyperbolic cosine function. The exponential function maps the real numbers onto the non-negative real numbers. The exponential function is an entire function, which means that it is differentiable for all x and its derivative is nonzero for all x. The exponential function is a periodic function with period 2. The exponential function is defined for real arguments x by the power series: It is a special case of the natural logarithm, which is the inverse function of the exponential function. In mathematics, the exponential function is the function ex, where "e" is the base of natural logarithms.
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