MYP 4Year 10Term 2
Functions
Domain & range · Composition · Inverses
Functions
15 objectives
Learning objectives
What students should be able to do by the end of this unit.
Function Notation and Representation
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- Understand the definition of a function as a rule that assigns each input exactly one output.
- Evaluate a function for a given input (e.g. find $f(3)$ given $f(x) = 2x - 5$).
- Solve equations of the form $f(x) = k$ to find inputs that give a chosen output.
- Substitute algebraic expressions into a function (e.g. find $f(a+1)$ or $f(2x)$).
- Move between numerical, algebraic, table and graphical representations of a function.
Domain, Range and Linear Functions
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- Identify the domain and range of a function from its graph.
- Find a sensible (natural) domain when a function is defined by a formula, including avoiding division by zero or square roots of negatives.
- Sketch and interpret linear functions, including those written as $f(x) = mx + c$.
- Sketch and interpret piecewise linear functions defined on different intervals.
- Use the vertical line test to decide whether a graph represents a function.
Composition and Inverses (Extended)
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- Form a composite function $f \circ g$ and evaluate it for given inputs.EXT
- Recognise that composition is not commutative ($f \circ g \neq g \circ f$ in general).EXT
- Find the inverse $f^{-1}(x)$ of a linear function algebraically.EXT
- Recognise that the graph of $y = f^{-1}(x)$ is the reflection of $y = f(x)$ in the line $y = x$.EXT
- Verify an inverse by showing $f(f^{-1}(x)) = x$.EXT
Review pack
Curated revision materials parents and students can download.
A review pack for this unit is being prepared.