Functions & Input/Output Tables: Education and Income Vocabulary Review

Vocabulary Review Sheet

Lesson – Functions & Input/Output Tables: Education and Income

How to Use

• Review each vocabulary word before your quiz.
• Compare the math, real-life, and fairness examples to understand how functions describe patterns in education and income.
• Keep this sheet in your Equity in Numbers Student Journal to revisit when analyzing data or creating graphs.
• Remember: Every input connects to an output — and every opportunity should connect to fairness.

Function

• Definition: A rule that links each input to exactly one output.
• Math Examples:
  • (y = 2x + 3)
  • Education → Income (High School → $34K, Bachelor’s → $62K)
• Real-Life Example: Each education level has one typical income value.
• Fairness Example: When two groups have different outputs for the same input, math exposes inequality in opportunity.

Input

• Definition: The starting value or “cause” in a function — what goes into the rule.
• Math Examples:
  • Education level = input; (x) in (y = f(x))
• Real-Life Example: High School, Associate, Bachelor’s, Master’s degrees.
• Fairness Example: Everyone can have the same input (education), but not everyone gets the same output (income).

Output

• Definition: The result or “effect” that comes out after applying the rule to the input.
• Math Examples:
  • (y = 2x + 3 → y = 7) when (x = 2).
  • Income earned from a specific education level.
• Real-Life Example: Bachelor’s degree → $62K average income.
• Fairness Example: Comparing outputs shows if equal education leads to equal pay.

Input/Output Table

• Definition: A chart that organizes inputs and outputs to show a function’s pattern.
• Math Examples:

Input (x)	Output (y)
1	3
2	5
3	7

• Real-Life Example:

Education	Income
HS Diploma	$34K
Bachelor’s	$62K

• Fairness Example: Side-by-side tables for different groups highlight income gaps at identical education levels.

Ordered Pair (x, y)

• Definition: Two related values showing one input and its matching output.
• Math Examples:
  • (HS, 34K), (Bachelor’s, 62K)
  • (x, y) = (2, 7)
• Real-Life Example: (Education, Income) points plotted on a graph.
• Fairness Example: Comparing points for different groups shows how opportunity lines rise or flatten unequally.

Rule or Function Rule

• Definition: The mathematical relationship connecting each input to its output.
• Math Examples:
  • (y = 10x + 20) or “add 10 each time.”
• Real-Life Example: Every extra level of education adds roughly $10,000 to average income.
• Fairness Example: If one group’s rule grows slower, math reveals systemic inequities affecting income.

Graph of a Function

• Definition: A visual model showing how outputs change as inputs increase.
• Math Examples:
  • A line rising from (1, 34) to (4, 78).
• Real-Life Example: A graph showing how income rises with higher degrees.
• Fairness Example: Two lines with different slopes (one steeper, one flatter) illustrate unequal returns on education.

Relationship

• Definition: The way inputs and outputs are connected; can show positive or negative trends.
• Math Examples:
  • As education ↑, income ↑ → positive relationship.
• Real-Life Example: More schooling usually means more income.
• Fairness Example: Math helps identify when the same education doesn’t yield the same reward — an inequitable relationship.

Gap (or Difference)

• Definition: The amount one output is greater or smaller than another.
• Math Examples:
  • (62K – 50K = 12K) income gap.
• Real-Life Example: Two people with bachelor’s degrees earn $12K apart.
• Fairness Example: Gaps measure the size of inequality; closing them means progress toward fairness.

Equity

• Definition: Fairness that ensures everyone receives the support they need to reach equal outcomes.
• Math Examples:
  • Adjusting a function’s rule so outputs align fairly.
• Real-Life Example: Creating programs that raise incomes for groups historically underpaid.
• Fairness Example: Equity in math mirrors equity in life — balancing the outputs when inputs are equal.

Summary of Math + Fairness Connections

Concept	Math Focus	Fairness Connection
Function & Rule	Links each input to one output	Reveals unequal outcomes for equal education
Input/Output Table	Organizes data	Visualizes opportunity gaps
Graph & Relationship	Shows patterns of growth	Highlights where inequity widens
Gap (Difference)	Measures change between outputs	Quantifies unfairness
Equity	Balances results	Promotes fair opportunity for all learners