Functions: Finding the Average Rate of Change

Functions: Finding the Average Rate of Change

How to find the Average Rate of Change:

• Use the formula:                     $m=\frac{y_2-y_1}{x_2-x_1}\$   

•  $y_{2\ }and\ y_1\ =\ outputs\ of\ the\ function.$  

•  $x_2\ and\ x_1\ =\ inputs\ of\ the\ function\$  

• Outputs should be directly over their cooresponding input.

Multiple Choice

Practice: Which Formula is set up correctly given:

y-values: 5 and 9

x-values: 3 and 8

• $m=\frac{9-5}{8-3}$

• $m=\frac{8-3}{9-5}$

Multiple Choice

Practice: Which formula is setup correctly give:

Outputs (y-values): -4 and 10

Inputs (x-values): -6 and -2

• $m=\frac{-2-\left(-6\right)}{10-\left(-4\right)}$

• $m=\frac{10-\left(-4\right)}{-2-\left(-6\right)}$

Multiple Choice

Practice: Which Formula is set up correctly given:

Outputs: 21 and 30

Inputs:  $-3\le x\le5$   

•  $m=\frac{5-\left(-3\right)}{30-21}$  

•  $m=\frac{30-21}{5-\left(-3\right)}$  

Multiple Choice

Practice: Which Formula is set up correctly given the coordinate point (x,y): (6, 13) and (7, 15)

• $m=\frac{15-13}{7-6}$

• $m=\frac{13-6}{15-7}$

Multiple Choice

Practice: Which Formula is set up correctly given

 $f\left(x\right)=2x^2$  over the interval  $-2\le x\le4$  

•  $m=\frac{32-8}{4-\left(-2\right)}$  

•  $m=\frac{32-8}{\left(-2\right)-4}$  

Solving Average Rate of Change problems.

Now that we have practiced setting up the formula. Lets do some practice problems.

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