Functions, transformations and inverses

Chapter 30 of 34 strong

RESTS ONSubstitute known values into a formula and evaluate it correctlyCH 4 Multiplication and divisionCH 9 Multiply and divide fractionsCH 1 Remove the greatest common numerical and algebraic factor from every term before considering any further factorisationCH 6 Simplify a fractionCH 1Recognise and factor a difference of two squares, a perfect-square trinomial, and a sum or difference of two cubes, with the correct sign patternFOUNDATIONSSolve equations with unknowns on both sides by collecting them onto one sideCH 1 Solve a one-step linear equationCH 7Test whether a matrix product is defined from the inner numbersFOUNDATIONSSolve equations with the unknown inside a fraction by clearing the denominator firstCH 9 Determine whether each input in a relation has exactly one output; on graph data, apply the vertical-line testCH 2Identify the vertex, horizontal axis, opening direction, intercepts, domain and range of a translated and dilated sideways parabola relation, and identify that the full relation is not a functionFOUNDATIONS

Composite functions and functional equations

Function transformations

Matrix transformations

Inverse functions and relations

Inverse compositions and intersections

Interpret (f∘g)(x) as f(g(x)), identify the inner and outer function and the order of application, and distinguish composition from multiplication and from the reversed composition

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Practise this

RESTS ON

Interpret f, f(x), image, preimage, rule, domain and co-domain; evaluate a function at a stated exact input and solve a simple equation of the form f(x)=cNot started

UNLOCKS

Form the rule for a composite by substituting the complete inner rule into every occurrence of the outer variable, simplify the result exactly, and state the domain of the compositeDecide whether a composition is defined by checking the exact subset condition ran inner ⊆ dom outer, and name the direction in which the check fails when it failsIdentify the inner and outer functions of a composite, differentiate each, multiply the outer derivative evaluated at the inner function by the inner derivative, and write the result in the requested factorised form CH 6