Question 10: Indicate whether each graph specifies a function y = f(x):

Solution

From vertical line test, (a) is a function because vertical lines drawn anywhere on the graph hit the graph only on one point. Similarly, curve (b) is also a function. Draw a vertical line any where on the graph and see it hits the curve on a single point. Curve (c) is, however, not a function. Vertical lines may hit the graph on more than one point (3 points, for example). So it is not a graph of a function.

Vertical line test? The vertical line test is a method to determine whether a curve is the graph of a function or not. Draw vertical line(s) at suitable place(s) on the curve. If any of them cuts the curve of function on more than two places, then the given curve is not a function. If the curve represents a function it would be cut only on one place by any of the vertical lines. Check your understanding: A line is called a linear function. All types of lines are functions, except one. Can you say which type of line will not be a function? Hint: Think about the y-axis.