Quiz 1: Piecewise Application

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.

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

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

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

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

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

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

For which of the following statements is the ONE-TO-ONE 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.HSF-BF.B.4C

Which of the following statements is considered NOT a piecewise funtion?

• Circle Form

  x² + y² = 1

• Quadratic Form

  F(x) = ax² + bx + c

• Linear Form:

  F(x) = ax + b

• Constant Form:

  F(x) = k

Tags

CCSS.HSF-IF.C.7B

• 19

• 40
  

• 30
  

• 9

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2