The function that describes the total cost of buying š„ hotdog sandwiches is š¶ š„ = 20š„. Evaluating š¶ 8 gives a cost of ā±160
Learning Objectives: At the end of this lesson, you should be able to solve problems involving functions
Example 1
A hotdog store on a street sells a hotdog sandwich that costs ā±20. Represent the cost š¶ of buying š„ number of hotdog sandwich. Using this function, solve for the cost of buying 8 hotdog sandwiches.
Example 2
A barangay captain wanted to enclose a rectangular piece of land next to a river using 100 meters of fencing materials. Represent the area š“ of the rectangular piece of land in terms of its length, š„. Solve for the area given that the length is 45 meters.
Solution for Example 2
The perimeter of the land is š„ + 2š¦. Since the perimeter is 100 meters, the equation is š„ + 2ļæ½ļæ½ = 100. The area of the land can be calculated based on this equation
Try ThisāØ
An accessories store on a mall sells a necklace that costs ā±300. Represent the cost šŖ of buying š number of necklace. Using this function, solve for the cost of buying 6 pieces of necklace.
A barangay captain wanted to enclose a rectangular piece of land next to a river to avoid the residents from getting to the river because it is too deep. He intends to use 200 meters of fencing materials to enclose the land.
Solving for the volume of the box if the width measures 5 inches
š = 4(5)^2 - 8(5) = 100 - 40 = 60 cubic inches
Representing the area šØ of the rectangular piece of land in terms of its width, š
š“ = ļæ½ļ潚¦
The perimeter of the land is š„ + 2š¦ = 100
Volume of a rectangular box
š = length Ć width Ć height
Replacing š¦ in terms of š„
š¦ = 100 ā š„ / 2
Constructing a function š that represents the volume of the box
š = 4ļæ½ļæ½(š„ā 2) = 4š„^2 - 8š„
Solving for the area of the land when the length is 45 meters
š“ 45 = 1,237.5 m^2
Area of a rectangular land
š“ = ļæ½ļ潚¦
The length of a rectangular box is five times its width while its height is 2 inches more than its width
A van can be rented for ā±2500 for 12 hours or less. An additional charge of ā±100 per hour is charged if the van will be rented for more than 12 hours
Volume of the box if the width measures 4 inches is 300 cubic inches
Construct a function V that will represent the volume of the box
Construct a function V that represents the cost of renting the van in terms of the number of hours t
To solve for the volume of the box given that the width is 5 inches, evaluate V(5)
Volume of the box is 300 cubic inches
Volume of the box is V = 4x^2(x-2)
If t > 12, the cost will be ā±2500 plus ā±100 per hour in excess of 12 hours. The excess hour can be expressed as t - 12. Thus, the second expression is 2500 + 100(t - 12)
How much will be charged if the van is rented for 18 hours is ā±2700
The desired piecewise function for V is V(t) = 2500 if 0 < t ā¤ 12, 2500 + 100(t - 12) if t > 12
If 0 < t ā¤ 12, the cost will be ā±2500. Thus, the first expression of the piecewise function is simply 2500 (a constant)
Volume of a rectangular prism is the product of its length, width, and height
Conditions for the piecewise function V
Volume of the box
V = lwh
Construct a function š that represents the cost of renting the van in terms of the number of hours š”
š š” = ā±3 000 if 0 < š” ā¤ 12 and š š” = ā±3 000 + ā±150(ļæ½ļæ½ - 12) if š” > 12
When the van is rented for 18 hours, the total cost is ā±3 100
The desired piecewise function will be š š” = 2 500 if 0 < š” ā¤ 12 and š š” = 2 500 + 100 ļæ½ļæ½ ā 12 if š” > 12
A van can be rented for ā±3 000 for 12 hours or less. An additional charge of ā±150 per hour is charged if the van will be rented for more than 12 hours
Construct a function ļæ½ļæ½ that represents the cost of a tricycle ride in terms of the number of kilometers, šāØ
š š = ā±20 if 0 < š ā¤ 3 and š š = ā±20 + ā±3(š - 3) if š > 3
A tricycle ride costs ā±20 for the first 3 kilometers. An amount of ā±3 is charged for every kilometer in excess of 3 kilometers
Excess hour
š” ā 12 (actual time š” minus 12 hours is the excess hour)
For š” > 12, the cost will be ā±2 500 plus ā±100 per hour in excess of 12 hours