GRE Prep: Function Shapes

Introduction

• Instructor: Tyler from Manhattan Prep
• Topic: Function shapes in GRE quantitative comparisons
• Platform: Live in Zoom, session uploaded to YouTube

Interaction

• Participants joined from various locations (NY, TX, CA, etc.)

Problem Solving Intros

• Example question to engage participants
• Technique: Function visualization for faster problem-solving

Basic Concepts

Linear Functions

• Graph Shape: Straight line
• Example: y = x

Even Powers (e.g., Squared)

• Graph Shape: Parabolic (U-shaped)
• Example: y = x²

Odd Powers (e.g., Cubic)

• Graph Shape: Curved (S-shaped)
• Example: y = x³
  • Curve flips for negative x values

Domain of X

• Visualizing function graphs help identify where one function is less than or greater than another
• Example: x³ < x
  • Graph shows x (linear) and x³ (cubic)
  • Identify where x³ is less than x (positive fractions, negatives more negative than -1)
• Compare these values within quantity comparison questions

Advanced Comparisons

Odd vs. Odd Powers

• Example: x³ vs. x⁵
• Identify where one function is greater than the other using graphs

Even vs. Even Powers

• Example: x² vs. x⁴
• Identify comparison points by graph intersection points and intervals

Mixed Powers (Even vs. Odd)

• Example: x vs. x²
• Recognize intervals where a linear function is greater or less than a quadratic function

Modifiers to Functions

Absolute Value

• Makes the function non-negative
• Example: |y| = |x|

Negative Multiplication

• Flips the function over the x-axis
• Example: -y vs. y

Practice Problems

Incorporating Modifiers

• Graph and compare functions with and without absolute values and negative signs

Generalizing Effects of Modifiers

• Absolute values prevent functions from dipping below the x-axis
• Negative signs flip the function vertically over the x-axis
• Application: Solve problems using graphs drawn with these modifiers

Advanced Problem Examples and Solutions

• Several exercises to solidify understanding
• Strategies: Simplify upfront info, use graph to determine domain, graph transformations based on modifiers

Summary & Key Takeaways

• Function Shape Types: Linear, parabolic (even powers), cubic (odd powers)
• Common Modifiers: Absolute value, negative multiplication
• Apply these visuals and transformations to solve GRE quantitative problems efficiently

Closing

• Resource Links: Further free prep hours, first session of the new course available free
• Encouragement: Engage with more materials available for further practice and prep