Function Notation
Function C gives the cost, in dollars, of buying n apples. What does each expression or equation represent in this situation?
a. C(5) = 4.50
Five apples cost $4.50.
Function w gives the weight of a cat, in kilograms, when it is m months old. Which statement represents the meaning of the equation w(7) = 4 in this situation?
The cat weighs 4 kilograms when it is 7 months old.
Function f is defined by the equation f(x) = x2 . (Lesson 4-4)
a. What is f(2)?
b. What is f(3)?
f(2) = 4
f(3) = 9
What is the Equation for calculating the average rate of change.
Write on the board.
The cost for an upcoming field trip is $30 per student. The cost of the field trip C, in dollars, is a function of the number of students x. Select all the possible outputs for the function defined by C(x) = 30x.
A. 20
B. 30
C. 50
D. 90
E. 100
B. 30
D. 90
Function C gives the cost, in dollars, of buying n apples. What does each expression or equation represent in this situation?
C(2)
The cost of 2 apples.
Functions A and B give the population of City A and City B, respectively, t years since 1990. In each function, population is measured in millions.
Here are the graphs of the two functions (#5)
Which function value is greater:
A(4) or B(4)?
b. Are there one or more values of t at which the equation A(t) = B(t) is true? If so, which one or which ones?
c. Identify at least two values of t at which the inequality B(t) < A(t) is true.
Function f is defined by the equation f(x) = x2 . (Lesson 4-4)
c. Explain why f(2) + f(3) ≠ f(5).
f(2) + f(3) = 4 + 9, which is 13. The value of f(5) is 25. Because 13 ≠ 25, we know that f(2) + f(3) ≠ f(5).
Jada walks to school. The function D gives her distance from school, in meters, t minutes since she left home. (Lesson 4-2) Which equation tells us “Jada is 600 meters from school after 5 minutes”?
D(5) = 600
A rectangle has an area of 24 cm2. Function f gives the length of the rectangle, in centimeters, when the width is w cm. Determine if each value, in centimeters, is a possible input of the function.
3 0.5 48 -6 0
Possible: 3, 0.5, and 48 are possible inputs. Not possible: -6, 0.
A number of identical cups are stacked up. The number of cups in a stack and the height of the stack in centimeters are related. (Lesson 4-1)
a. Can we say that the height of the stack is a function of the number of cups in the stack? Explain your reasoning
Yes. For every number of cups, there is one height in centimeters
The table and the graph show the population of a country between 2010 and 2015.
Find the average rate of population growth between 2010 and 2015
0.52 million people per year, or 520,000 people per year
The average rate of population growth between 2013 and 2015 is 0.35 million people per year. If the population continues to grow at this rate, in which year will it reach 40 million? Explain your reasoning. (Question 7B)
The average rate of change between 2013 and 2015 is 0.35 million people per year. If the population continues to grow at this rate, the population will be 39.45 million in 2016, 39.80 million in 2017, and 40.15 million in 2018. So the population will reach 40 million between 2017 and 2018.
Jada walks to school. The function D gives her distance from school, in meters, as a function of time, in minutes, since she left home. What does D(10) = 0 represent in this situation?
After 10 minutes, Jada is 0 meters from school. She is at school after 10 minutes.
Two functions are defined by the equations f(x) = 5 − 0.2x and g(x) = 0.2(x + 5). Select all statements that are true about the functions. (Lesson 4-5)
A. f(3) > 0
B. f(3) > 5
C. g(-1) = 0.8
D. g(-1) < f(-1)
E. f(0) = g(0)
A, C, D.
Solve each system of equations without graphing. Show your reasoning.
(- 5x + 3y = - 8)
( 3x − 7y = - 3)
(2.5, 1.5). Sample reasoning: Multiplying the first equation by 3 and the second equation by 5 gives:
In a function, the number of cups in a stack is a function of the height of the stack in centimeters. (Lesson 4-1) a. Sketch a possible graph of the function on the coordinate plane. Be sure to label the axes.
Use White Board.
Question 7C
How does the average rate of change of the population from 2013 to 2015 compare to that from 2011 to 2013? Explain what this means in terms of the population of the country.
The two average rates of change are equal, both are 0.35 million people per year. This means during those periods, the population grew at the same rate each year
The percent of voters between the ages of 18 and 29 that participated in each United States presidential election between the years 1988 to 2016 are shown in the table.
The function P gives the percent of voters between 18 and 29 years old that participated in the election in year t.
a. Determine the average rate of change for P between 1992 and 2000.
P(t) decreased 1.025% per year between 1992 and 2000.
The graph of function f passes through the coordinate points (0,3) and (4,6). Use function notation to write the information each point gives us about function f.
f(0) = 3 and f(4) = 6
Function R gives the amount of rain measured by a rain gauge t hours since it started raining. The amount of rain is measured in millimeters.
a. What does each expression or equation represent in this situation?
i. R(3)
ii. R(0.5) = 14
The amount of rain 3 hours after it started raining.
One-half hour after it started raining, the amount of rain was 14 millimeters.
The owner of a small restaurant bought 75 kilograms of rice. Each week, the restaurant uses 4.5 kilograms of rice. Function r gives the remaining amount of rice, in kilograms, as a function of the number of weeks since the restaurant owner bought the rice.
a. Complete the table
(Check #6)
Priya bought two plants for a science experiment. When she brought them home, the first plant was 5 cm tall and the second plant was 4 cm. Since then, the first plant has grown 0.5 cm a week and the second plant has grown 0.75 cm a week.
a. Which plant is taller at the end of 2 weeks? Explain your reasoning.
The first plant is taller because 5 + 0.5(2) > 4 + 0.75(2).
Pick two different values of t so that the function has a negative average rate of change between the two values. Determine the average rate of change.
t = 2008 and t = 2012 with the average rate of change
40.9 − 48.4 /2012 − 2008 = - 1.875.
The average rate of change is -1.875% per year.
To raise funds for a trip, members of a high school math club are holding a game night in the gym. They sell tickets at $5 per person. The gym holds a maximum of 250 people. The amount of money raised is a function of the number of tickets sold. Which statement accurately describes the domain of the function?
A. all numbers less than 250
B. all integers
C. all positive integers
D. all positive integers less than or equal to 250
D. all positive integers less than or equal to 250