Functions: Domain, Codomain, and Range · Semester 1

Graph Transformations

Students will apply vertical and horizontal translations to quadratic graphs and sketch the resulting graphs.

Key Questions

  1. 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?
  2. Explain why the order of successive transformations is significant, and construct a rational function example where reversing the order yields a different graph.
  3. 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.

MOE Syllabus Outcomes

MOE: Functions and Graphs - Secondary 3MOE: Graphing Techniques - Secondary 3
Level: JC 1
Subject: Mathematics
Unit: Functions: Domain, Codomain, and Range
Period: Semester 1

Suggested Methodologies

Problem-Based Learning

Tackle open-ended problems without predetermined solutions

35–60 min

Learn more about Problem-Based Learning

Inquiry Circle

Student-led investigation of self-generated questions

30–55 min

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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.

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Graphing Rational and Exponential Functions

Students will sketch graphs of linear and quadratic functions, identifying key features like intercepts and turning points.

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Graphs of Modulus Functions

Students will apply reflections across the x-axis to quadratic graphs and sketch the resulting graphs.

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