Maths-
General
Easy

Question


Tell whether each graph is a function and justify your answer. Which graph is not a good representation of a real world situation? Explain.

The correct answer is: 2, 6 and 8


    Hint:
    An equation of the form y = f(x) is called a function if there is a unique value of y for every value of x. In other words, every value of x must have one value of y. We can check if the graph is a function by the vertical line test. A graph represents a function if any vertical line in the xy plane cuts the graph at maximum one point.
    Step by step solution:
    The first graph is

    We check if the graph is a function by vertical line test.
    When we draw a vertical line at x = 4, it cut the graph at 3 points.
    Thus, graph A is not a function.
    Graph B is

    We can observe that any vertical line on the plane cuts the graph at maximum one point.
    Thus, the above graph is a function.
    In graph A, at time t = 4, we can see that d has three values, which are 2, 6 and 8.
    This means that at the same time t=4, the distances travelled are 2, 6 and 8, which is physically impossible. There can be only one value of distance associated with a value of time which is the case in graph B.
    Thus, graph A is not a good example of a real world situation.
    Note:
    In a function, every value of x must have one value of y. When we draw a vertical, it cuts x axis at one point, we take that point to be x. If the vertical line cuts the graph at two points, then it gives two values of y for one value of x. This does not represent a function.

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