Graphing Rational and Exponential Functions
Students will sketch graphs of linear and quadratic functions, identifying key features like intercepts and turning points.
About This Topic
Students will sketch graphs of linear and quadratic functions, identifying key features like intercepts and turning points.
Key Questions
- How do vertical and horizontal asymptotes arise from the algebraic structure of a rational function, and how do they constrain the graph's behaviour in those regions?
- Compare the long-run behaviour of rational functions where the degree of the numerator exceeds, equals, or is less than that of the denominator, and explain how each case determines the type of asymptote.
- Analyse how transformations of y = e^x or y = 1/x alter key features such as asymptotes, intercepts, domain, and range, and sketch the resulting graphs.
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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.
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