A function is any equation where for any input in the equation, the output yields exactly one value. Typically, the input is called x and the output is called y.
Functions are best understood by examples. First, consider the equation y = x?. Given an x, the square of x only yields one value for y. This is a function.
Next, consider the equation y? = x. Given an x, there can be two possibilities for y. If x is 4, y can be either positive or negative 2. This is not a function, since y can be more than one value with a given x.
Learn MoreIn math, the sine of an angle is defined as the length of the side of a right triangle opposite the acute angle divided by the length of the hypotenuse. The lengths of these sides can be determined through the Pythagorean Theorem.
Full Answer >The Bernoulli differential equation is y^t + p(x)y = q(x)y^n. On the interval being worked on, p(x) and q(x) are continuous functions, and n is a real number.
Full Answer >The equation for the spring force is k = -F/x. This equation is derived from Hooke’s Law, which states that the force needed to extend or compress a spring a certain distance is proportional to that distance. The equation for Hooke’s Law is F=kx, where k is the spring constant.
Full Answer >The vector equation of a line is r = a + tb. In this equation, "a" represents the vector position of some point that lies on the line, "b" represents a vector that gives the direction of the line, "r" represents the vector of any general point on the line and "t" represents how much of "b" is needed to get from "a" to the position vector.
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