Function Notation
Graph Features
Average Rate of Change
Word Problems Tables and Graphs
100
Function W gives the weight of a puppy, in pounds, as a function of its age, t, in months.
What does W(2)=5 mean in this context?
At two months, the puppy weighed 5 pounds.
100
A ball bounces several times after it is dropped. The graph shows the height of the ball, in meters, t seconds after it is dropped.
From what height was the ball dropped? What part of the graph tells us that?
vertical intercept/6 ft.
100
Is there a time when the populations were the same? If so, when?
Yes, around 1935.
100
An option for purchasing a gaming console comes with a monthly gaming subscription to the online service and is represented by the function C, where
C(x)= 5x+260
Find C(10) and determine what it means in this context.
C(10)=310. Using the gaming system and online service for 10 months after the free trial will cost $310.
200
Function g represents the gallons of gas in a gas tank after driving d miles. What does the following statement mean?
g(8)= 30.2
After driving 8 miles, there are 30.2 gallons of gas in the tank.
200
A ball bounces several times after it is dropped. The graph shows the height of the ball, in meters, t seconds after it is dropped.
True or false: The function reaches its maximum height after the first bounce.
False
200
Is there a time, t, that satisfies the inequality below where function T represents Texas and function C represents California? If so, what value of x?
T(x)>C(x)
anytime when x<1930
200
A slushy kiosk bought 100 kg more ice. Each week, the kiosk uses 6.5 kg of ice. Function W gives the remaining amount of ice in kg, as a function of the number of weeks, x, since they bought more ice.
Complete the table:
(5, 67.5)
(10, 35)
x: -6.5x+100
300
Function S gives the amount of snow measured in inches, t hours after it started snowing.
What does the following expression mean in this context?
S(6.5)
The amount of snow six and a half hours after it started snowing.
300
A ball bounces several times after it is dropped. The graph shows the height of the ball, in meters, t seconds after it is dropped.
True or false: The x-intercepts show when the ball hits the ground.
True
300
Between which interval is the population changing the fastest?
Between 1910 and 1920
300
Graph the function that is represented by the table below.
400
Function S gives the amount of snow measured in inches, t hours after it started snowing.
Use function notation to show that there was the same amount of snow after 5 hours as there was after 10 hours.
S(5)=S(10)
400
A ball bounces several times after it is dropped. The graph shows the height of the ball, in meters, t seconds after it is dropped.
True or False: There are multiple times when the function is at its minimum value.
True
400
What is the average rate of change in Texas between the years 1960-2000?
Texas' population increased by 250,000 people per year between the years 1960-2000.
400
This table shows the population of a country between years 2010 and 2015. What is the average rate of change between the years 2010 and 2014? 
0.6 million people per year or 600,000 people per year
500
Function S gives the amount of snow measured in inches, t hours after it started snowing.
Use function notation to show that 90 minutes after it started snowing, there were 2 inches of snow measured.
S(1.5)=2
500
For what value of t makes this statement true?
h(t)=2
t=1.865
500
What is the average rate of change in CA between the years 1950 and 1970?
the population increased by 500,000 people per year between 1950 and 1970.
500
A slushy kiosk bought 100 kg more ice. Each week, the kiosk uses 6.5 kg of ice. Function W gives the remaining amount of ice in kg, as a function of the number of weeks, x, since they bought more ice. Solve the equation W(x)=22 and explain what the solution means in this context.
x=12. After 12 weeks, the kiosk will have 22 kg of ice remaining.