Finding Rate of Change

Finding the Average Rate of Change!

​We will find the average rate of change (A.R.C.) from function

1. Tables

2. Graphs

3. Equations

Happy learning!

​Take a minute to think...

Multiple Choice

What are the x-values they are talking about?

• $$x=6\ and\ x=18$$

• $$x=12\ and\ x=24$$

• $$x=19\ and\ x=49$$

• $$x=49\ and\ x=29$$

Multiple Choice

Which is the correct math to find the average rate of change?

• $$\frac{29-49}{6-18}$$

• $$\frac{18-6}{49-29}$$

• $$\frac{49-29}{18-6}$$

• $$\frac{29-49}{18-6}$$

Multiple Choice

What is the average rate of change?

• $$-\frac{5}{3}$$

• $$-\frac{3}{5}$$

• $$\frac{5}{3}$$

• $$\frac{3}{5}$$

Multiple Choice

What is the average rate of change?

• $$-\frac{1}{2}$$

• $$\frac{3}{5}$$

• $$\frac{5}{3}$$

• $$\frac{3}{2}$$

Drag and Drop

The average rate of change is ​ ​

Placeholder

Drag these tiles and drop them in the correct blank above

9

Drag and Drop

The average rate of change is

Placeholder

Drag these tiles and drop them in the correct blank above

Open Ended

How would you find the average rate of change of the graph? What are you concentrating on?

Drag and Drop

The coordinates are ( $$-9$$ ,​

Placeholder

​ )

and ( $$1$$ ,​

Placeholder

).

Drag these tiles and drop them in the correct blank above

Multiple Choice

What is the average rate of change?

• $$\frac{2}{5}$$  

• $$\frac{5}{2}$$  

• $$-5$$  

• $$-1$$  

• $$-3$$  

Drag and Drop

The coordinates are ( $$-3$$ ,​

Placeholder

​ )

and ( $$3$$ ,​ ​

Placeholder

).

Drag these tiles and drop them in the correct blank above

Multiple Choice

What is the average rate of change?

•   $$\frac{2}{5}$$

•   $$\frac{5}{2}$$

• $$1$$  

• $$-1$$  

• $$-3$$  

Open Ended

Given the function $$h\left(x\right)=-x^2-x+5$$ determine the average rate of change of the function over the interval $$-6\le x\le2$$ .

How will you do this?

Multiple Choice

Given the function $$h\left(x\right)=-x^2-x+5$$ determine the average rate of change of the function over the interval $$-6\le x\le2$$ .

• $$\frac{-1--25}{2--6}=\frac{24}{8}=3$$

• $$\frac{-25--1}{6--2}=-\frac{24}{8}=-3$$

• $$\frac{2--6}{-25--1}=\frac{8}{-24}=-\frac{1}{3}$$

Multiple Choice

Given the function $$f\left(x\right)=x^2+3x-1$$ , determine the average rate of change of the function over the interval $$-3\le x\le4$$ .

• $$\frac{4--3}{27--1}=\frac{7}{28}=\frac{1}{4}$$

• $$\frac{-1-27}{4--3}=\frac{-28}{7}=-4$$

• $$\frac{27--1}{4--3}=\frac{28}{7}=4$$

Open Ended

What do $$\frac{\Delta y}{\Delta x}$$ , $$\frac{change\ of\ output\ values}{change\ of\ input\ values}$$ , $$\frac{y_2-y_1}{x_2-x_1}$$ and $$\frac{f\left(b\right)-f\left(a\right)}{b-a}$$ all have in common?