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.

part b: write one example of a linear function and one example of a non-linear function. (use x and y as the variables)

use full sentences and explain fully.

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,

An example is or or etc

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

180

step-by-step explanation: