i think you are missing the word point in the question, and if so, then yes. the domain of a function describes what you can put into it, and since your putting x values into the function, if there is a point that exists at a certain x value, then that x is included in the domain.
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I'm not sure what exactly you're asking about, but if you're asking about the difference between relations and functions, here's the answer.In a relation, a value in the domain may have one or more values in the range. That is, for every x on graph there may be more than one value of y. In terms of word problems and such, x is the independent variable (i.e. time) and y is the dependent variable (i.e. temperature). Basically, if you graph a relation, you can draw a vertical line anywhere on the graph and that line may intersect one or more points on the graph. A circle or a horizontal parabola is a relation, not a function.In a function, for every value in the domain there is only one value in the range. That is, for every value of x there is one and only one value of y. If you draw a vertical line anywhere on the graph of the function, it will only intersect the graph once. If it intersects the graph more than once, then that graph is not a function. An example of a function would be a vertical parabola, a line, or a cubic.Hope that helps.
Both the function "cos x" and the function "sin x" have a maximum value of 1, and a minimum value of -1.
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Assuming the standard x and y axes, the range is the maximum value of y minus minimum value of y; and the domain is the maximum value of x minus minimum value of x.
The graph or function relates a value y (in the vertcal direction) to a value x (in the horizontal direction). For each point x in the domain, there must be one and only one value y. In terms of a graph that means that a vertical line from any value of x in the domain must meet the graph in exactly place - at least once and not more than once. More than one x values can have the same y value associated with them.
The definition of a function is "A relation in which exactly one element of the range is paired with each element of the domain." This means that in the relationship of a function, each range element (x value) can only have one domain element (y value). If you draw a vertical line and it crosses your graph twice, then you can see that your x value has two y values, which is not a function.
A graph is represents a function if for every value x, there is at most one value of y = f(x).
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Any equation which maps each value of x in the domain to a value in the range is a function of x.
Consider the graph of y= +/- sqrt(x). Notice that, for any value of x greater than 0, there are two values of this relation. To be a function a relation has to assign one value in the range to each value in the domain. So this cannot be a function, yet it has a perfectly ordinary graph.
Any equation which maps each value of x in the domain to a value in the range is a function of x.