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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