This comprehensive worksheet is designed to sharpen the graphing skills of Algebra 2, Pre-Calculus, and AP/IB Calculus students. Mastering the ability to sketch and analyze the graphs of parent functions and their transformations is a non-negotiable prerequisite for success in differential and integral calculus.

This resource provides targeted practice on five fundamental function families:

1. $f(x) = x^2$ (Quadratic)
2. $f(x) = x^3$ (Cubic)
3. $f(x) = \frac{1}{x}$ (Rational)
4. $f(x) = \sqrt{x}$ (Square Root)
5. $f(x) = |x|$ (Absolute Value)

🎯 Key Features and Skills Covered

• Graphing Functions in Vertex/Standard Form: Students practice sketching transformed functions like $g(x) = -3(x-3)^2$, requiring them to apply multiple transformations simultaneously.
• Comprehensive Transformations: Problems incorporate all key transformation types:
  
  • Reflections: Across the x-axis and y-axis.
  • Stretches/Compressions: Vertical and Horizontal scaling.
  • Translations: Shifting the graph vertically and horizontally.

• Multiple-Choice Practice: The format mirrors standardized tests, requiring students to carefully analyze and select the correct sketch from multiple options (as shown in the sample image).
• Focus on Key Features: Practice involves correctly identifying and plotting the vertex, axis of symmetry, endpoints, and asymptotes (for the rational function).