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Linear Functions, Tables, and Models

SAT MathAlgebraMedium

Interpret function notation and build linear rules from patterns.

What you need to know

  • f(x) names the output produced by input x.
  • A constant first difference for equal x-steps indicates a linear function.
  • Initial value is the output at input 0.
  • A context determines meaningful domain and range.

The AYLOTI method

  1. Find change in output over change in input.
  2. Use one row or point to determine the intercept.
  3. Write f(x) = mx + b.
  4. Check the rule against another value and interpret parameters.

AYLOTI • Sir Hunain Zia • SAT Score 1594/1600 • 154 Total A Grades (Personal), 11 World Records, 7 Distinctions

Worked example

A table contains (0, 7), (2, 13), and (5, 22). Find f(x).

  1. Slope from first two points: (13 − 7)/(2 − 0) = 3.
  2. At x = 0, output is 7, so b = 7.
  3. Rule: f(x) = 3x + 7; it gives 22 at x = 5.

Answer: f(x) = 3x + 7.

Common SAT traps

  • Using Δx/Δy instead of Δy/Δx.
  • Assuming the first listed output is the intercept when x ≠ 0.
  • Ignoring a restricted contextual domain.
Quick check

If f(x) = 5x − 4, find f(3).

11.

Before you move on

  • Explain the core rule without looking back.
  • Redo the worked example using your own steps.
  • Write the trap you are most likely to fall for.
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