Function Notation
Analyzing Graphs
Comparing Graphs
Rate of Change
Domain and Range
100
Function c gives the cost of parking, in dollars, when a car is parked for h hours. What is the meaning of c(2)=5?
It costs $5 to park for 2 hours.
BE CAREFUL NOT TO SWITCH THE ORDER AROUND!
100
Tyler filled up his bathtub, took a bath, and then drained the tub. The function B gives the depth of the water, in inches, t minutes after Tyler began to fill the bathtub. Complete the following statement:
B(0)= ____
B(0)=0
100
Here are descriptions of four situations in which the volume of water in a tank is a function of time. Match each description to a corresponding graph.
A: An empty 20-gallon water tank is filled at a constant rate for 3 minutes until it is half full. Then, it is emptied at a constant rate for 3 minutes.
B: A full 10-gallon water tank is drained for 30 seconds, until it is half full. Afterwards, it gets refilled.
C: A 2,000-gallon water tank starts out empty. It is being filled for 5 hours, slowly at first, and faster later.
D: An empty 100-gallon water tank is filled in 50 minutes. Then, a dog jumps in and splashes around for 10 minutes, letting 7 gallons of water out. The tank is refilled afterwards.
A: 3
B: 1
C: 2
D: 4
100
Here is the graph of a function.
Which time interval shows the largest rate of change?
A: From 0 to 2 seconds
B: From 0 to 3 seconds
C: From 4 to 5 seconds
D: From 6 to 8 seconds
C: From 4 to 5 seconds
100
A child tosses a baseball up into the air. On its way down, it gets caught in a tree for several seconds before falling down to the ground.
The graph represents the height of the ball, h, as a function of time, t.
Describe the range.
All values between 0 and 12.
200
Function C gives the cost, in dollars, of buying n apples.
What does C(10)=9 mean?
10 apples cost $9.
BE CAREFUL NOT TO SWITCH THE ORDER AROUND!
200
Function V gives the volume of water (liters) in a water cooler as a function of time, t (minutes).
Find the value or values of t that make V(t)=4 true. Explain what the value or values tell us about the volume of the water in the cooler.
t=2 and t=6.1
At 2 and 6.1 minutes, the water volume in the cooler was 4 liters.
200
This graph shows the populations of Baltimore and Cleveland in the 20th century. B(t) is the population of Baltimore in year t. C(t) is the population of Cleveland in year t.
Which function value is greater: B(1920) or C(1920)?
C(1920)
200
A family bought a used car that had been driven 12,000 miles.
The table shows the total distance, in miles, that the car has traveled each year since the purchase.
Find the average rate of change over the 3 years.
The family drives about 3,250 miles per year.
200
A child tosses a baseball up into the air. On its way down, it gets caught in a tree for several seconds before falling down to the ground.
The graph represents the height of the ball, h, as a function of time, t.
Describe the domain.
All values between 0 and 8.5.
300
Function D gives the distance a person walked in kilometers, as a function of time, t, in minutes, since the walk began.
Use function notation to represent the following statement:
45 minutes after the person started walking, they had traveled 3 kilometers.
D(45)=3
300
A child tosses a baseball up into the air. On its way down, it gets caught in a tree for several seconds before falling down to the ground.
The graph represents the height of the ball, h, as a function of time, t.
What does the vertical intercept represent?
The height of the ball was 5 feet before it was tossed.
300
This graph shows the populations of Baltimore and Cleveland in the 20th century. B(t) is the population of Baltimore in year t. C(t) is the population of Cleveland in year t.
Are there values of t at which the equation B(t)=C(t) is true? If so, which ones?
Yes, around t=1910 and t=1942.
300
Using the graph, find the average rate of change of the state of California from 1970 to 1990.
0.5 million people per year.
300
The graph shows the attendance at a sports game as a function of time in minutes.
Describe the domain.
All values between 0 and 70.
400
Function D gives the distance a person is from their house in kilometers, as a function of time, t, in minutes, since the walk began.
Use function notation to represent the following statement:
The distance from the house 25 minutes after starting the walk was the same as the distance 55 minutes after starting the walk.
D(25)=D(55)
400
A child tosses a baseball up into the air. On its way down, it gets caught in a tree for several seconds before falling down to the ground.
The graph represents the height of the ball, h, as a function of time, t.
What does the horizontal intercept represent?
The ball hit the ground after about 8.5 seconds.
400
Identify at least two values of x at which the inequality g(x)<f(x) is true.
Any two values between 4 and 9.
400
The average rate of population growth for Texas between 2000 and 2010 is 0.4 million people per year. If the population continues to grow at this rate, in which year would you expect it to reach 27 million?
Around 2015.
2010 - 25 million
2011 - 25.4 million (25+0.4)
2012 - 25.8 million (25.8+0.4)
2013 - 26.2 million
2014 - 26.6 million
2015 - 27 million
400
The graph shows the attendance at a sports game as a function of time in minutes.
Describe the range.
All WHOLE NUMBERS between 0 and 55.
(It is important that the range is only whole numbers since the y-axis represents the number of people.)
500
Function T gives the temperature in degrees Fahrenheit, h hours since midnight.
What does T(4) represent in this situation?
The temperature 4 hours after midnight or at 4 am.
500
A tennis ball is dropped from an initial height of 30 feet. It bounces 5 times. Which of the following statements are true?
A. The function has no minimum value
B. There are multiple times when the function is at its minimum value
B is true.
500
Complete the following statements:
a. R(0)=
b. D(0)=
c. R(t)=0 when t=
d. D(t)=0 when t=
a. R(0)=25
b. D(0)=0
c. R(t)=0 when t=5
d. D(t)=0 when t=7
500
The graph shows the total distance, in feet, walked by a person as a function of time, in seconds.
Was the person walking faster between 0 and 40 seconds or between 100 and 160 seconds?
0 and 40 seconds
500
Two children set up a lemonade stand in their front yard. They charge $1 for every cup. They sell a total of 15 cups of lemonade. The amount of money the children earned, R dollars, is a function of the number of cups of lemonade they sold, n.
Is 20 part of the domain of this function? Explain your reasoning.
No, they only sell a total of 15 cups of lemonade.