Rational Functions and Community Budgeting – Lecture Vocabulary

This set contains 52 vocabulary flashcards covering mathematical concepts such as ratios, functions, polynomials, and rational functions, plus key terms from the community budgeting scenario presented in the lecture.

Ratio

A comparison of two quantities, often expressed as a fraction.

Fraction

A number written with a numerator over a denominator to show parts of a whole.

Function

A relation where each input has exactly one output.

Input

The independent value substituted into a function.

Output

The dependent value produced by a function for a given input.

Relation

Any set of ordered pairs connecting inputs to outputs.

Polynomial

An algebraic expression with variables and coefficients combined by addition, subtraction, multiplication, and non-negative integer exponents.

Variable

A symbol, usually a letter, that represents an unknown or changeable value.

Coefficient

The numerical factor multiplied by a variable in an algebraic term.

Non-Negative Integer Exponent

A whole-number power (0, 1, 2, …) used in polynomial terms.

Rational Function

A function that is the ratio of two polynomials, r(x) = p(x)/q(x) with q(x) ≠ 0.

Polynomial Function

A function whose rule is given by a polynomial expression.

Numerator

The top number in a fraction, showing the part being considered.

Denominator

The bottom number in a fraction, showing the total number of equal parts.

Domain (Rational Function)

All real x-values for which the denominator of a rational function is not zero.

Example Rational Function f(x)

f(x) = 2/(x + 1)(x – 2) – a ratio of polynomials shown in the notes.

Example Rational Function g(x)

g(x) = 3x/(x + 4) – a rational function from the lecture examples.

Example Rational Function h(x)

h(x) = 5/(2x + 1) – another sample rational function provided.

Barangay

The smallest administrative unit in the Philippines, similar to a village.

Relief Goods

Essential items like rice, canned food, chicken, and hygiene kits distributed to families in need.

Budget

An itemized plan for income and expenditure over a specific period.

Approximation

An estimated value used when exact figures are unknown.

Pledge

A promised donation of money or goods for a cause.

Survey

A systematic collection of data to determine actual numbers, such as families in a barangay.

Mathematical Model

An equation or expression that represents a real-world situation.

Equation

A mathematical statement showing that two expressions are equal.

Total Budget

The complete sum of money available for a project or operation.

Per-Family Allocation

The amount of resources each family receives after equal division.

Fixed Cost

An expense that does not change with the level of production, such as rent.

Variable Cost

An expense that changes proportionally with production volume.

Operational Cost

The combined fixed and variable expenses required to run a business.

Average Cost

Total cost divided by the number of units produced.

Tee-rific Prints

The small-scale T-shirt printing business used in the lecture’s cost example.

Bake-A-Wish

The local bakery featured in the custom cake cost example.

Custom Cake

A specially designed cake with specific ingredients and labor costs.

Equipment Maintenance

Regular servicing costs to keep machines running properly.

Utilities

Monthly expenses for electricity, water, and other essential services.

Rent

A fixed payment made for using a building or space.

Ingredients

The raw materials used in producing food items like cakes.

Labor

Human work effort, often costing money per unit produced.

Cash Donation

Monetary aid given to support relief operations.

Donation in Kind

Goods or services contributed instead of money.

Actual Number of Families

The real count of households determined after a detailed survey.

Equal Division

Distributing resources so each recipient receives the same share.

Stranded Resident

A person unable to leave the barangay who must be included in aid planning.

Transferred Residency

A family that has moved in or out, affecting the total beneficiary count.

Relief Operations

Organized efforts to distribute aid during emergencies.

Community Cooperation

Residents working together, in cash or kind, to address common problems.

One-Week Supply

Relief goods intended to last a family for seven days.

Rice

A staple grain included in the barangay’s relief package.

Hygiene Kit

Basic sanitary supplies such as soap and toothpaste distributed during relief.

Model for Relief Budget

Amount per family = Total budget ÷ Number of families, a rational function in the scenario.

Example Cost Function

C(x) = 5000 + 15x for Tee-rific Prints, combining fixed and variable costs.

Average Cost Function

Ā(x) = (Fixed cost + Variable cost·x) / x, a rational model used in the practice problems.