Maths-
General
Easy

Question

The average rate of change of a function is less from x= 1 to x= 4 than from x= 5 to x= 8 . What type of function could it be? Explain.

hintHint:

1. When the difference between 2 consecutive output values (y values) for a given constant change in the input values (x values) is constant. i.e. y(n)- y(n-1) is constant for any value of n, the function is known as a linear function.
2. When the difference between 2 consecutive differences for output values (y values) for a given constant change in the input values (x values) is constant. i.e. dy(n)- dy(n-1) is constant for any value of n, the function is known as a quadratic function.
3. When the ratio between 2 consecutive output values (y values) for a given constant change in the input values (x values) is constant i.e. fraction numerator straight y left parenthesis straight n right parenthesis over denominator straight y left parenthesis straight n minus 1 right parenthesis end fraction is constant for any value of n, the function is known as an exponential function.

The correct answer is: The given function is a polynomial function i.e. either a quadratic function or an exponential function.


    Step-by-step solution:-
    From the above definitions, we can conclude that the rate of change of a Linear function function is constant.
    Hence, the given function is not a Linear Function.
    For both the remaining types of function i.e. Quadratic function as well as exponential function, the rate of change may increase at a constant rate (for Quadratic equations) or an exponential rate (for exponential function).
    From the given information, we do not know the rate of increase in the function between x = 1 to x = 4 and x = 5 to x = 8.
    Hence, the given function could be a quadratic function or an exponential function, which are both polynomial function.
    Final Answer:-
    ∴ The given function is a polynomial function i.e. either a quadratic function or an exponential function.

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