Question

Part A: A graph passes through the points (0, 2), (2, 6), and (3, 12). Does this graph represent a linear function or a non-linear function? Explain your answer in words.

Answer 1

Answer:

Step-by-step explanation:

Part A

The graph passes through .

If the graph that passes through these points represents a linear function, then the slope must be the same for any two given points.

Using  and .

We obtain the slope to be

Using  and .

We obtain the slope to be

.

Since the slope is not constant(the same) everywhere, the function is non-linear.

Part B

A linear function is of the form

where  is the slope and  is the y-intercept.

An example is

A linear function can also be of the form,

where  and  are constants.

An example is

A non linear function contains at least one of the following,

Product of  and

Trigonometric function

Exponential functions

Logarithmic functions

A degree which is not equal to  or .

An example is  or or  etc