Function Notation
Function QQ gives a puppy’s weight in pounds as a function of its age in months.
What does the expression Q(18) represent?
The weight of the puppy when it was 18 months old.
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 & D
Function f gives the temperature, in degrees Celsius, t hours after midnight.
Choose the equation that represents the statement: “At 1:30 p.m., the temperature was 20 degrees Celsius.”
A: f(1:30)=20
B: f(1.5)=20
C: f(13:30)=20
D: f(13.5)=20
D
Noah's cousin is exactly 7 years younger than Noah. Let C represent Noah's cousin's age and N represent Noah's age. Ages are measured in years.
C=N−7 The input is N, Noah's age, and the output is C, his cousin's age.
Solve for n. 30=-5(6n+6)
-2
Function QQ gives a puppy’s weight in pounds as a function of its age in months.
What does Q(30) = 27.5 represent in this situation?
When the puppy was 30 months old, it weighed 27.5 pounds.
Select all the possible input-output pairs for the function y=x3.
A: (-1,-1)
B: (-2,-8)
C: (3,9)
D: (12,18)
E: (4,64)
F: (1,-1)
A, B, & E
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.
Explain the meaning of the following statement.
B(0)=0
The bathtub was empty when Tyler began to fill the tub
Noah's cousin is exactly 7 years younger than Noah. Let C represent Noah's cousin's age and N represent Noah's age. Ages are measured in years.
N=C+7. The input is C, and the output is N.
Solve for x.
37=-3 + 5(x+6)
2
Use function notation to represent the statement.
When the puppy turned 12 months old, it weighed 19.6 pounds.
Q(12)=19.6
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
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.
Explain the meaning of the statement in this situation.
B(1)<B(7)
At 1 minute, the tub has less water than at 7 minutes.
The store sells book for $9 each and charges $5 for shipping.
Write the inverse function of this scenario.
n = T-5/9
Solve for x.
5(2x+6)=-4(-5 - 2x) +3x
10
Use function notation to represent the statement.
When the puppy was a months old, it weighed w pounds.
Q(a)=w
S=4n+2 represents the number of seats, S, as a function of the number of tables, n.
What domain makes sense for this function?
All whole numbers.
Function f gives the temperature, in degrees Celsius, t hours after midnight.
Use function notation to write an equation or expression for the statement.
The temperature at 12 p.m.
f(12)
The store sells books at p dollars and charges $5 for shipping.
Write the inverse function.
n = (T-5)/p
Solve the system of equations.
-7x+2y=18
6x + 6y = 0
(-2,2)
An art museum opens at 9 a.m. and closes at 5 p.m. The function V gives the number of visitors in a museum hours after it opens.
Explain what this statement tells us about the situation: V(1.25)=28.
An hour and 15 minutes after the museum opened (at 10:15 a.m.), there were 28 visitors in the building.
S=4n+2 represents the number of seats, S, as a function of the number of tables, n.
What range makes sense for this function?
All numbers that are 2 more than multiples of 4.
Function f gives the temperature, in degrees Celsius, t hours after midnight.
Use function notation to write an equation or expression for the statement.
The temperature was the same at 9 a.m. and at 4 p.m.
f(9)=f(16)
The store sells books at at p dollars and charges f for shipping.
Write the inverse function.
n = (T - f)/p
Solve the system of equations.
-8x-10y=24
6x+5y=2