Given a graph of a function, explain how to find the rate of change and how to determine whether it is a linear or nonlinear function.

A linear function is represented using a straight line.

To calculate the rate of change of a function, pick any two points on the graph and apply the following formula for rate of change

Take for instance:

The rate of change (m) is:

So, the rate of change is 2

To check if the function is linear or not.

Pick another point on the graph, then calculate the slope using the same formula.

Let another point be:

The rate of change using the following points:

and

is as follows:

Since the rate of change is unchanged (i.e. 2) in both computations, then the function is linear.

If the value changes, then the function is nonlinear.

Read more about linear and nonlinear functions at:

link

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet