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Topic 3: Functions and relations

Introduction to functions and relations

5 hours

• Understand the concept of a relation as a mapping between sets, a graph and as a rule or a formula that defines one variable quantity in terms of another.
• Recognise the distinction between functions and relations and use the vertical line test to determine whether a relation is a function. 1 interactive
• Recognise and use function notation, domain and range, and independent and dependent variables.
• Recognise and use piece-wise functions as a combination of multiple sub-functions with restricted domains.
• Model and solve problems that involve piece-wise functions with and without technology.

Graphs of relations

4 hours

• Recognise and determine features of the graphs of 𝑥2 + 𝑦2 = 𝑟2 and (𝑥 − ℎ)2 + (𝑦 − 𝑘)2 = 𝑟2, including their circular shapes, centres and radii. 1 interactive
• Recognise and determine features of the graph of 𝑦2 = 𝑥, including its parabolic shape and axis of symmetry.
• Recognise and determine features of the graphs of 𝑦 = 𝑎√𝑥 − ℎ + 𝑘, including their shape, intercepts, and behaviour as 𝑥 → ∞ and 𝑥 → − ∞.
• Sketch the graphs of relations, with and without technology.
• Model and solve problems that involve relations, with and without technology.

Reciprocal functions

2 hours

• Recognise features of the graphs of 𝑦 = 1 𝑥 and 𝑦 = 𝑎 (𝑥−ℎ)+ 𝑘, including their hyperbolic shape, intercepts, asymptotes, and behaviour as 𝑥 → ∞ and 𝑥 → − ∞. 1 interactive
• Model and solve problems that involve reciprocal functions, with and without technology.
• Sketch the graphs of reciprocal functions, with and without technology.