The curve is a graph of a function of x. If so, find the domain and range of the function.
The curve is the graph of a function of x.
Vertical line test states that the curve in the xy coordinate plane is the graph of the function of x if and only if a vertical line intersects the curve at exactly one point.
Perform the vertical line test for the given graph.
Draw a vertical line such that it passes through the curve as shown below in Figure 1.
It is observed from Figure 1 that the vertical line intersects the curve exactly at one point. Therefore, the curve is the graph of a function of x.
Since, the domain of a function is the set of all possible x values of the graph, the domain of the function is .
Since, the range of a function is the set of all possible y values of the graph, the range of the function is .
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