Functions: Finding the Average Rate of Change

Functions: Finding the Average Rate of Change

How to find the Average Rate of Change:

​you are given two x-values: -3 and -1 <-- these are x₁ and x₂

you plug those x-values into the function to get the corresponding y-values (y₁ and y₂)

example

step 1: Plug in 2 (x₁) to the function to get out y₁
3(2)⁵-2(2)²+7 = 95

step 2: Plug in 5 (x₂) to the function to get out y₂
3(5)⁵-2(5)²+7 = 9332

step 3: fill in x₁ and x₂ in the denominator (these are the number given at the beginning) and fill in y₁ and y₂ to the numerator (the numbers you got after plugging in the x's to the given function)

​f(x) = 3x⁵ - 2x² + 7 [2, 5]

How to find the Average Rate of Change:

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:  $$-3\le x\le6$$   

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

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

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  $$-2\le x\le4$$  

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

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

Fill in the Blank

Find the average rate of change of f(x) = 2x² + 2 from [−1, 0 ].

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