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5 of 5 objectives have lessons · 0 studied · 0 secure
What Cambridge says you should be able to do, in our words. Codes are the topic number plus the objective’s position.
Understand the terms function, domain, range, one-one function, inverse function and composition of functions.
Taught in: Composite functions, Functions, domain and range, Inverse functions, One-one functions and the horizontal line test · 6 questions
Identify the range of a given function in simple cases, and find the composition of two given functions.
Examples: the range of f : x ↦ 1/x for x ≥ 1, and the range of g : x ↦ x² + 1 for x ∈ ℝ. Includes the condition that a composite function gf can only be formed when the range of f lies within the domain of g.
Taught in: Composite functions, Functions, domain and range, The range of a quadratic function · 14 questions
Determine whether or not a given function is one-one, and find the inverse of a one-one function in simple cases.
Example: finding the inverse of h : x ↦ (2x + 3)² − 4 for x < −3/2.
Taught in: Inverse functions, One-one functions and the horizontal line test · 10 questions
Illustrate in graphical terms the relationship between a one-one function and its inverse.
Sketches should indicate the mirror line y = x.
Taught in: Graphs of a function and its inverse · 7 questions
Understand and use the transformations of the graph of y = f(x) given by y = f(x) + a, y = f(x + a), y = af(x) and y = f(ax), and simple combinations of these.
Includes using the terms 'translation', 'reflection' and 'stretch' to describe transformations. Questions may involve algebraic or trigonometric functions, or other graphs with given features.
Taught in: Transformations: combining two, Transformations: reflections, Transformations: stretches, Transformations: translations · 23 questions