**References**

Problem 2:

Piece-wise Function

An online shop based in Manila,

charges a fee for shipping services within or outside Manila. They charge an initial shipping fee of P100.00 for orders with a total value of P400.00 and under, an additional P50.00 shipping fee for orders with a total value between P400.00 and P800.00 and, a doubled initial shipping fee is charged for orders with a total value above P800.00.

b. How much shipping fee will they charge if the total value of orders are P500.00

**Functions with Real Life Situations**

f(x) =

Problem 1:

Piece-wise Function

In Punta Isla Lake Resort, a boat ride cost

P500.00 intended for 15 passengers only. Additional passengers are charged P50.00 per head. Use a piece-wise function to represent the boat ride fare.

Let x be the cost of the boat ride.

**{ }**

500, 0 < x ≤ 15

500 + 50( x -15 ) , x > 15

Supposed there are 18 passengers,

f(18) = 500 + 50( x - 15 )

= 500 + 50( 18 - 15 )

= 500 + 50( 3 )

= 500 + 150

= 650

f(x) =

{ }

500, 0 < x ≤ 15

500 + 50( x -15 ) , x >15

The total boat ride fare for 18 passengers is P650.00.

a. Write a piecewise function representing the shipping fee charge (f) in pesos for (x) total value of orders.

f(h) =

**{ }**

100, if 0 < x ≤ 400

100(2) , if x > 800

f(x) =

**{ }**

f(x) = 100 + 50

= 150

They will charge P150.00 shipping fee.

Problem 3:

Piece-wise Function

A photocopy shop charges P1.00 per

photocopy for orders of 20 or fewer photocopies, P0.85 per photocopy for orders of 50 or fewer but more than 20 photocopies, and P0.75 per photocopy for orders of more than 50 photocopies. Write a function representing the cost f in pesos for x number of photocopies.

Problem 3:

Piece-wise Function

f(x) =

{ }

1(x), if 0 < x ≤ 20

0.85(x), if 21≤ 50

0.75(x), if x > 50

f(x) =

{ }

1(x), if 0 < x ≤ 20

0.85(x), if 21≤ 50

0.75(x), if x > 50

a. How much will you pay if you order 34 photocopies?

f(x) = 0.85(x)

= 0.85(34)

= 28.9

You will pay P28.90 if you order 34 photocopies.

b. How much will you pay if you order 55 photocopies?

1(x), if 0 < x ≤ 20

0.85(x), if 21≤ 50

0.75(x), if x < 50

f(x) =

{ }

f(h) = 0.85(x)

= 0.85(55)

= 46.75

You will pay P47.75 if you order 55 photocopies.

**END**

**OF**

**REPORT**

Belandres, Francis

Deanon, John Paul

Faraon, Kaith

Julao, Stephany

Valente, Fe

GROUP 6 MEMBERS:

100 + 50, if 400<x≤800

100, if 0 < x ≤ 400

100 + 50, if 400<x≤800

100(2), if x > 800

Problem 4:

Piece-wise Function

Rental car charges flat fee of P300.00

plus an additional P5.00 per mile when the number of miles driven is less than or equal to 100 miles. For any miles over 100, the company reduces the price to P2.50.

a. Write a piecewise function.

f(x) =

**{ }**

300 + 5(x), if 0 < x ≤ 100

2.50 ( x – 100) + 800, if x > 100

f(x)=

{ }

300 + 5(x), if 0 < x ≤ 100

2.50 ( x – 100) + 800, if x > 100

b. How much will they charge you if you have driven 150 miles?

f(x) = 2.50 (x-100) + 800

f (150) = 2.50 ( x - 100) + 800

f (150) = 2.50 ( 150 - 100) + 800

= (2.50) (50) + 800

= 925

Problem 5:

Piece-wise Function

In a certain tourist destination, a

horseback ride costs P150.00 for the first 5 km., and for every km. added costs an additional P40.00.

a. Write a piecewise function for the problem.

f(x) =

**{ }**

150 , if 0 < x ≤ 5

150 + 40 ( x – 5), x > 5

{ }

f(x) =

150 , if 0 < x ≤ 5

150 + 40 ( x – 5), x > 5

b. How much will a 10 km. horseback ride cost?

f(x) = 150 + 40 (x – 5 )

f(10) = 150 + 40 (10 – 5)

= 150 + 40(5)

= 150 + 200

= 350

A 10 km. horseback ride costs P350.00.

They will charge you P925.00 if you have driven 150 miles.

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