Top 10 Most Common Functions: A Tier List

Overview

A fun and informative tier list ranking of ten common mathematical functions, focusing on their characteristics and applications.

Linear Function

• Equation: $y = x$
• Characteristics:
  • Constant rate of change (slope is the same between any pair of points).
  • Easy to graph using slope (rise over run).
• Applications:
  • Calculating income from hourly wages.
  • Temperature conversions.
  • Distance formula ($distance = speed \times time$).
• Tier: A

Quadratic Function

• Equation: $y = x^2$
• Characteristics:
  • Graph forms a parabola.
  • Symmetrical with an absolute max or min (vertex).
• Applications:
  • Projectile motion.
  • Revenue optimization.
• Tier: A

Square Root Function

• Equation: $y = \sqrt{x}$
• Characteristics:
  • Restricted domain (only one quadrant).
  • Graph resembles square root symbol.
  • Negative x yields an imaginary number.
• Applications:
  • Trigonometry, statistics, and physics formulas.
  • Distance formula, quadratic formula, standard deviation, period of simple harmonic motion.
• Tier: C

Absolute Value Function

• Equation: $y = |x|$
• Characteristics:
  • Never negative.
  • Turns negative values positive.
• Tier: F

Sine Function

• Equation: $y = \sin(x)$
• Characteristics:
  • Range between -1 and 1.
  • Infinite solutions for x.
  • Connections to the unit circle.
• Applications:
  • Tidal patterns, vibrations, temperature, sound waves, simple harmonic motion, voltage.
  • Trigonometric identities.
• Tier: S

Rational Function

• Equation: $y = \frac{1}{x}$
• Characteristics:
  • Has asymptotes.
  • Engages with concepts of limits and infinity.
• Tier: B

Exponential Function

• Equation: $y = 2^x$
• Characteristics:
  • Demonstrates exponential growth.
  • Significant in financial and biological contexts.
• Applications:
  • Radioactive decay, compound interest, half-life, population growth.
  • Illustrates power of exponential growth.
• Tier: B

Logarithmic Function

• Equation: $y = \log(x)$
• Characteristics:
  • Analyzes values with a wide range of magnitudes.
  • Inverse of exponential functions.
• Applications:
  • Richter scale, sound intensities, pH levels.
• Tier: C

Cubic Function

• Equation: $y = x^3$
• Characteristics:
  • Rotational symmetry.
  • Difficult to graph accurately.
• Tier: F

Constant Function

• Equation: $y = 3$
• Characteristics:
  • Always the same output for any input.
  • Zero slope, predictable.
• Tier: S

Conclusion

The tier list reflects the presenter's unique perspective on the usefulness and interest of each function, considering their mathematical properties and real-world applications.