This comprehensive package includes two dynamic worksheets designed to help students master the concept of function transformations using graphical representations. Ideal for Algebra II, Pre-Calculus, or introductory College Algebra courses, this resource provides essential practice in connecting algebraic notation with visual shifts, reflections, and stretches.

Worksheet 1: Describing Transformations (Problems)

• Focus: Students analyze the relationship between the parent function $f(x)$ (solid line) and the transformed function $g(x)$ (dashed line).
• Task: Students must identify and correctly describe the sequence of transformations (shifts, reflections, vertical/horizontal stretches/compressions) necessary to map $f(x)$ onto $g(x)$.
• Skill: Reinforces the understanding of the order of transformations and the impact of signs and constants on the graph.

Worksheet 2: Writing the Equation (Problems 9-12)

• Focus: Students work in reverse—analyzing the graph to write the correct function rule.
• Task: Given the graphs of $f(x)$ and $g(x)$, students must select the correct equation for $g(x)$ in terms of $f(x)$ (e.g., $g(x) = f(x+1) + 3$).
• Skill: Connects graphical features (like the location of vertices, axes of symmetry, and key points) directly to algebraic notation.