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Maths-

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Easy

Question

How can you determine whether a linear , exponential or quadratic function best models the data ?

hint 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. $fraction numerator straight y left parenthesis straight n right parenthesis over denominator straight y left parenthesis straight n minus 1 right parenthesis end fraction$ is constant for any value of n, the function is known as an exponential function.

The correct answer is: 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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