Unit 2 Review: Function Notation and AROC

Unit 2 Review

Function Notation and Average Rate of Change

Function Notation

using F(x) "F of x" instead of y

Examples

you try:  $f(x)=3(4)^x$  find  $f\left(2\right)$  

Multiple Choice

 $f\left(x\right)=x^2+7$  find  $f\left(-2\right)$  

• 3

• 11

• 5

• -5

Multiple Choice

 $h(x)=\frac{12}{x}$  

Find h(24)

• 3

• 1/2

• 36

• 1/4

Multiple Choice

 $f\left(x\right)=-2x+5$  
 $g\left(x\right)=100\left(\frac{1}{4}\right)^x$  
Find f(4) + g(2) 

• 3.25

• -2.61

• 7.2

• 1.39

Multiple Choice

Find f(3) using the graph of f(x)

• 2

• 3

• 4

• 1

Multiple Choice

Using the graph of f(x) find f(2)-f(0)

• 0

• 1

• 2

• 3

What is Average Rate of Change?

• The average rate of change is finding how much something changes over time. 

• This is like finding the slope of a line given specific points

• The average rate of change is not constant like slope is, meaning it changes throughout the graph.

Multiple Select

Which formulas can be used to find average rate of change from [a,b]

Check all that apply 

• rise/run

•  $\frac{y_2-y_1}{x_2-x_1}$  

•  $\frac{f\left(b\right)-f\left(a\right)}{b-a}$  

• y=mx+b

Graphically

First look at the graph on the right. Find the average rate of change from [-3, 1]

Algebraically

Now look at the equation on the left. Find the average rate of change from [-3, 1]

Multiple Choice

Oscar planted a tomato seed in his garden. Each day he recorded the height of the tomato plant.

During which interval did the tomato plant grow the fastest?

• Day 4 to Day 6

• Day 8 to Day 10

• Day 6 to Day 8

• Day 10 to Day 12

Multiple Choice

What is the average rate of change from day 2 to day 14?

• 3/2

• 9

• 4/3

• 3/4

Multiple Choice

What is the average rate of change fron [2,6]?

• 13/4

• -15

• 4/13

• 1/15

Multiple Choice

 $y=500\left(1.05\right)^x$  

According to the function above, to the nearest whole number what is the average rate of change over the interval from x=0 to x=10?

• 31

• -31

• 50

• 1.05