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.
Hint:
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. 
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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