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The graph of a sine and cosine function is an example of a function that has infinite domain and finite domain. The range is finite because these graphs have an amplitude, which is the maximum or minimum value on the graph. As for domain, the x-values are the pi-radians.

If our range is any real number value, we can say it spans from negative infinity to infinity, (−∞,∞). But more concisely, we use the symbol R to say the range is all real numbers. Infinities. When using interval notation for infinity we always use parentheses, since infinity isn’t a point.

To find the range we need to determine the y-values on the graph. Notice that the y-values on the graph start at 0 ( the lowest point of the graph), and if we visualize that the graph gets infinitely “taller” we can see the y-values go to positive infinity.

For the quadratic function f(x)=x2 f ( x ) = x 2 , the domain is all real numbers since the horizontal extent of the graph is the whole real number line. Because the graph does not include any negative values for the range, the range is only nonnegative real numbers.

u = union symbol (no overlap) n = overlap. Numbers included are part of the possible domain while excluded numbers are not part of the possible domain.

The domain is all x-values or inputs of a function and the range is all y-values or outputs of a function. When looking at a graph, the domain is all the values of the graph from left to right. The range is all the values of the graph from down to up.

In its simplest form the domain is all the values that go into a function, and the range is all the values that come out. But in fact they are very important in defining a function.