how do you? Classify Equation as Function?

Answer 1

a function is a given equation which has no repeating domain as in no repeating x values.

Answer 2

An "equation" equates things. A function is a specific kind of equation wherein there is but one thing on one side of the equation and one or more things on the other side of the equation. Let's look at the two items in detail.

An equation is like a teeter totter with a fulcrum or place where the teeter totter rocks around somewhere near the middle. To balance the teeter totter so it rests horizontal with the ground, you need to have equal forces on either side of the teeter totter fulcrum. Otherwise, the end with the greater force will crash to the ground leaving the other end of the teeter totter (and your partner) way up.

The equals sign (=) is the fulcrum of an equation. To keep the equation balanced the values (the forces) have to be equal on either side of the = sign. Otherwise the equation would be out of balance; the two sides of the = sign would not be equal. A stable, balanced equation might be, for example, 2 X 3 = 1 X 6; so its forces are the same on either side. Here the forces are 6 on both sides of the = sign.

One of the great features of a balanced equation is that we don't always need to know all the values on either side. We can actually use the balance requirement to calculate unknown values. For example, suppose 2 X 3 = 1 X y; where y is our unknown. We can see, because an equation must be balanced, y must equal 6; otherwise, the equation would not be balanced.

A function is simply a special equation. Strictly speaking, a function will have but one value on one side of the = sign, but it can have many values on the other side. The one value on one side is called the "dependent" value because it depends on all those values on the other side of the = sign. The values on the other side are called "independent" values because you can set them independently to whatever value you wish.

c = sqrt(a^2 + b^2) is an example of a function. c is the one dependent value (a variable) on the one side. a and b are the independent variables (values) on the other side. We call a, b, and c "variables" because their numeric values can vary over a range of values.

We can set a and b to whatever value we want, which is why we call them independent. But when we do, c has to be a specific value because it depends on a and b, and because this is a special kind of equation, the two sides of = have to remain in balance. For example, if we set a = 3 and b = 4, we have c = sqrt(9 + 16) = sqrt(25) = 5, which c has to be; otherwise the function, a special kind of equation, would be out of balance.

In math, there are all kinds of special functions. Things like sine and cosine, for example, are functions. y = sine(theta), for instance, will give the value of the dependent y for any value we might give to the independent variable theta. In this special case the range of values theta can be given is limited to -n(pi) ==> +m(pi), which is just math talk for saying theta has to be limited to some multiple of 360 degrees. Theta is an angle.

Other special functions, with special case handling, include Bessel, Gamma, Dirac Delta, and so on functions. But they all have one dependent variable and one or more independent variables.

Answer 3

If you draw a graph of the equation and there are points above one another (i.e. with the same x coordinate), then the equation is a function.

This is because a function has a different y for every x you enter.

Wikipedia explains it really well: