Graph Transformations
Students will apply vertical and horizontal translations to quadratic graphs and sketch the resulting graphs.
About This Topic
Students will apply vertical and horizontal translations to quadratic graphs and sketch the resulting graphs.
Key Questions
- How do the four standard transformations, y = f(x) + a, y = f(x + a), y = af(x), and y = f(ax), each affect asymptotes, intercepts, and the domain and range of a function?
- Explain why the order of successive transformations is significant, and construct a rational function example where reversing the order yields a different graph.
- Given the graph of y = f(x), apply a combination of transformations to sketch y = af(bx + c) + d, justifying each step in terms of geometric effect on key features.
Active Learning Ideas
See all activities→Activities & Teaching Strategies
See all activities
Planning templates for Mathematics
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
Unit PlannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
RubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
More in Functions: Domain, Codomain, and Range
Introduction to Functions: Input and Output
Students will understand functions as rules that assign a unique output to each input, using tables, graphs, and simple equations.
8 methodologies
Graphing Rational and Exponential Functions
Students will sketch graphs of linear and quadratic functions, identifying key features like intercepts and turning points.
8 methodologies
Graphs of Modulus Functions
Students will apply reflections across the x-axis to quadratic graphs and sketch the resulting graphs.
8 methodologies