DETERMINE IF THE ORDERED PAIR IS LINEAR EXPONENTIAL OR NEITHER

Linear function :

A linear function is a function whose graph is a line. Thus, it is of the form f(x) = mx + b where 'm' and 'b' are real numbers.

If the function is linear, then the difference between two immediate outputs will be equal.

Exponential function :

The function which is in the form y = ab^x

If the function is linear, then each output should be multiplied by the same constant throughout the outputs.

A function has the following coordinate points. Could the function represent a linear function, exponential function, or neither?

Problem 1 :

(1, 2), (2, 8), (3, 20)

Solution:

A constant change of +1 in x corresponds to different changes in y.

So, it is neither.

Problem 2 :

(10, 30), (11, 20), (12, 10)

Solution:

A constant change of +1 in x corresponds to a constant change of -10 in y.

Hence, the given set of ordered pairs represents linear function.

Problem 3 :

(13, 20), (14, 4), (15, 4/5)

Solution:

A constant change of +1 in x corresponds to an increase in y by a constant factor of 1/5.

Hence, the given set of ordered pairs represents exponential function.

Problem 4 :

(7, 6), (8, 12), (9, 20)

Solution:

A constant change of +1 in x corresponds to different changes in y.

So, it is neither.

Problem 5 :

(2, 1), (3, 4), (4, 16)

Solution:

A constant change of +1 in x corresponds to an increase in y by a constant factor of 4.

Hence, the given set of ordered pairs represents exponential function.

Problem 6 :

(5, 3), (6, 7), (7, 10)

Solution:

A constant change of +1 in x corresponds to different changes in y.

So, it is neither.

Problem 7 :

(3, -1), (5, 7), (7, 15)

Solution:

A constant change of +2 in x corresponds to a constant change of +8 in y.

Hence, the given set of ordered pairs represents linear function.

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