Maths-
General
Easy
Question
How can you determine whether a linear , exponential or quadratic function best models the data ?
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: To determine whether a linear, quadratic or exponential function best models the given data, we find the relation between 2 consecutive y values (output values).
Step-by-step solution:-
The first step in determining whether a table shows a linear, quadratic or exponential function is to find the relation (difference and ratio) between 2 consecutive output values of the given function.
On the basis of the relation between output values for a given constant change in the input values determine the type of a function.
If d is constant for all consecutive values of output (y), the function is a linear function,
If difference of ds is constant for all consecutive values of output (y), the function is a quadratic function and
If ratio is constant for all consecutive values of output (y), the function is a exponential function.
Final Answer:-
∴ To determine whether a linear, quadratic or exponential function best models the given data, we find the relation between 2 consecutive y values (output values).
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