EOC Review Lecture Notes

Understanding Functions

1. Linear Functions

   • Recognized by constant first differences in Y-values.
   • Example: Increases of 3 every time.

2. Exponential Functions

   • Recognized by consistent multiplication in Y-values.
   • Example: Multiplying by 4 each time.

3. Key Function Types

   • Linear, Exponential, and Quadratic functions are crucial.

Evaluating Functions

• Evaluate function for f(-3):
  • Substitute -3 for x.
  • Example: f(-3) = -8.

Quadratic Functions

1. Key Features

   • Vertex: Highest/lowest point.
     • Example: (-1, 4)
   • Axis of Symmetry: x = -1
   • Domain: All real numbers.
   • Range: Y ≤ 4
   • End Behavior: Y values go to -∞.

2. Increasing/Decreasing Intervals

   • Increasing until vertex.
   • Decreasing after vertex.

Solving Systems of Equations

• Elimination Method
  • Example: Eliminate x variable.
  • Solution: x = 2, y = 2.

Simplifying Expressions

• Positive Exponents Only
  • Example: x * y⁵ / 3*

Radical Expressions

• Simplify with One Radical
  • Example: 16 * ∛20*

Graphing Linear Equations

• Slope-Intercept Form
  • Slope = 3/4
  • Y-intercept = -2

Comparing Functions

• Slopes and Intercepts
  • Greater slope: G(x)
  • Greater Y-intercept: G(x)
  • Greater X-intercept: f(x)

Writing Inequalities

• Graph Interpretation
  • Example: y > -x - 2

Solving Absolute Value Equations

• Setup Two Equations
  • Example: x = 0, x = -1

Simple Interest Calculation

• Using Formula
  • Example: Amount = $577.50 after 10 years.

System of Equations in Word Problems

• Set up equations for costs
  • Example costs: Pants = $16.67, Shirts = $16.66

Parabola Equations

• Vertex and Point Usage
  • Equation example: y = -4x² + 24x - 32

Maximizing Profit with Quadratics

• Vertex Formula Usage
  • Example: $3.50 per ticket maximizes profit.

Perpendicular Lines

• Opposite Reciprocal Slopes
  • Equation example: y = -9/2x - 5

Exponential Functions

• End Behavior Description

  • As X → -∞, Y → -∞
  • As X → ∞, Y → 0

• Y-Value Changes

  • Y is increasing and getting closer to 0.