Quiz 1: Piecewise Application

Quiz
•
Mathematics
•
12th Grade
•
Medium
+2
Standards-aligned
Henry Phan
Used 1+ times
FREE Resource
10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
5 mins • 10 pts
If you were a single person in Connecticut in 2008 with a taxable income of x dollars then your state income tax T was determined by the rule” such as the model of the tax:
T(x) =
¶ 0.03x; if x ≤ 10,000
¶ 300 + 0.05(x - 10, 000) , if x > 10,000
Which of the following statement below is true
•A 3% tax applies to income if you earn at least $10,000.
•An additional 5% tax applies to any income with a maximum value of $10,000.•
•A 3% tax applies to income if you earn exactly $10,000.
•An additional 5% tax applies to any income different from $10,000.
•A 5% tax applies to income up to $10,000.
•An additional 3% tax applies to income exceeding $10,000.
•A 3% tax applies to income up to $10,000.
•An additional 5% tax applies to income exceeding $10,000.
2.
MULTIPLE CHOICE QUESTION
5 mins • 10 pts
A travel service charges a toll fee for crossing a bridge to a beach island, based on the type of vehicle:
•$8 for each sedan car.
•$9 for each minivan or pickup truck.
•$10 for each bus or RV.
Construct the piecewise function model.
C(x) =
•$8x ; (sedan)
•$9x; (van/truck)
•$10x; (bus/RV)
C(x) =
•$8; (sedan)
•$9; (van/truck)
•$10; (bus/RV)
C(x) =
•$8x for 1 car
•$9x. for 2 car
•$10x for more 2
•$8 for x≤ 1
•$9 for 1<x≤2
•$10 for x>2
3.
MULTIPLE CHOICE QUESTION
5 mins • 10 pts
A museum charge $5 per person for a guided tour with a group of 1 to 9 people or a fixed $50 fee for a group of 10 or more people. Write a function model relating the number of tour people. (Let C(x) is the charge, x is a number of people seing a museum)
C(x) =
⊪ $5; 1 ≤ x ≤ 9
⊪ $50; x ≥ 10
C(x) =
⊪ $5x; 1 ≤ x ≤ 9
⊪ $50; x ≥ 10
C(x) =
⊪ $5x; 1 < x < 9
⊪ $50; x > 10
C(x) =
⊪ $5; 1 < x < 9
⊪ $50x; x > 10
4.
MULTIPLE CHOICE QUESTION
5 mins • 10 pts
Construct a piecewise model: A city's water bill is calculated as follows:
⋙ A flat fee of $20 for usage up to 1,000 gallons.
⋙ $0.05 per gallon for usage between 1,001 and 5,000 gallons.
⋙ $0.10 per gallon for usage above 5,000 gallons.
C(x) =
⋙ $20x; x ≤ 1000
⋙ $20x + $0.05(x-1000); 1001 ≤x ≤ 5000
⋙ $20x + $0.05(x-1000) +0.1(x - 5000); x > 5000
C(x) =
⋙ $20x; x < 1000
⋙ $20x + $0.05(x-1000); 1000 < x < 5000
⋙ $20x + $0.05(x - 1000) +0.1(x - 5000); x ≥ 5000
C(x) =
⋙ $20; x ≤ 1000
⋙ $20 + $0.05(x-1000); 1001 ≤x ≤ 5000
⋙ $20 + $0.05(4000) +0.1(x - 5000); x > 5000
C(x) =
⋙ $20; x < 1000
⋙ $20 + $0.05(x-1000); 1000 < x < 5000
⋙ $20 + $0.05(4000) +0.1(x - 5000); x ≥ 5000
5.
MULTIPLE CHOICE QUESTION
5 mins • 10 pts
Construct a piecewise model: A mobile carrier charges for data usage as follows:
$30 flat rate for under 10 GB of data.
$2 per GB for data usage between 10 GB and 50 GB.
$5 per GB for data usage above 50 GB.
∇ $30; for x < 10
∇ $30 + 2(x -10); for 10 ≤ x ≤ 50
∇ $30 + 2(50-10) + 5(x - 50); for x > 50
∇ $30; for x ≤ 10
∇ $30 + 2(x -10); for 10 < x < 50
∇ $30 + 2(50-10) + 5(x - 50); for x ≥ 50
∇ $30x; for x < 10
∇ $30x + 2(x -10); for 10 ≤ x ≤ 50
∇ $30x + 2(x-10) + 5(x - 50); for x > 50
∇ $30x; for x ≤ 10
∇ $30x + 2(x -10); for 10 < x < 50
∇ $30x + 2(x-10) + 5(x - 50); for x ≥ 50
6.
MULTIPLE CHOICE QUESTION
5 mins • 10 pts
Construct a model: A shipping company charges for packages as follows:
A flat rate of $3 per pound for packages weighing up to 2 pounds.
$1 per pound for packages weighing more than 2 pounds and up to 10 pounds.
$2 per pound for packages weighing over 10 pounds.
⊫ 3x; for x < 2
⊫ (2*3), + 1(x - 2); for 2 ≤ x < 10
⊫ 6, + 1(10-2) + 2(x - 10); for x≥
10
⊫ 3x; for x ≤ 2
⊫ (2*3), + 1(x - 2); for 2 < x ≤ 10
⊫ 6, + 1(10-2) + 2(x - 10); for x >
10
⊫ 3; for x ≤ 2
⊫ 3, + 1(x - 2); for 2 < x ≤ 10
⊫ 3, + 1(10) + 2(x - 10); for x >
10
⊫ 3; for x < 2
⊫ 3, + 1(x - 2); for 2 ≤ x < 10
⊫ 3, + 1(10) + 2(x - 10); for x≥
10
7.
MULTIPLE CHOICE QUESTION
5 mins • 10 pts
For which of the following statements is NOT a function?
For x, y are the inputs and outputs
x = {a, b, c, d}
y = {s, t, u, v, w, x, y, z}
For x, y are the inputs and outputs
x = {s, t, u, v, w, x, y, z}
y = {a, b, c, d}
For x, y are the inputs and outputs
x = {s, t, u, v, w, x, y, z}
y = {a, b, c, d, e, f, g, h}
For x, y are the inputs and outputs
x = {s, t, u, v, w, x, y, z}
y = {a}
Tags
CCSS.8.F.A.1
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