# How Are Domain and Range of Parent Functions Determined?

The domain and range of parent functions can be determined by finding the values located farthest to the right, left, top and bottom of the graph. The domain of the graph includes the complete set of x-values while the range encompasses the suite of y-values. Together, the values in the domain and range form two lines, which are used to create the graph.

When graphed, the values of the domain appear as the horizontal line while the values of the function form the vertical line. The numbers in the domain are determined by first identifying the points farthest to the left and the right, which form the outermost limits of the horizontal line. Similarly, the extent of the vertical line, which contains values of the range, is determined by finding all possible y-values, which form the highest and lowest points of the graph’s vertical line. When graphed, lines contain the real numbers in the set of domain and range values. Real numbers in the domain may cover a large group of values and extend from negative ranges into positive ranges. Real numbers in the function, however, cannot extend into negative values, and therefore include values greater than or equal to zero.

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