Maths-
General
Easy

Question

Meri Approximates the area of circles using the equation  and records areas of circles with different radius lengths in a table.

a) Graph the ordered pairs from the table
b) Is the relation a function ? Explain.

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.

The correct answer is: graph is a function.


    Step by step solution:
    Let us denote the radius of the circle by x.
    Let us denote the area of the circle by y.
    Then the given table is
    x
    1
    2
    3
    4
    5
    y
    3
    12
    27
    48
    75
    We plot the above points in a graph.

    We can check if a 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. We use this method to check if the given graph represents a function.
    We can see that if we draw any vertical line in the xy plane, it cuts the graph at exactly one point.
    Hence, the given graph is a function.

    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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