Functions and relations

Chapter 60 of 34 strong

RESTS ONMultiplication and divisionCH 2Decimal place valueFOUNDATIONSSolve a one-step linear equationFOUNDATIONSSolve equations with unknowns on both sides by collecting them onto one sideCH 1 Check a claimed solution or point by substituting into the original equationCH 1 Compute a slope from a graph as rise over run between two pointsCH 1 Identify the intercept and slope in y = a + bx, including its edge shapesCH 1Find the constant of variation for a stated inverse relationshipFOUNDATIONSTranslate a described situation into a linear equation in one unknownCH 1 RoundingCH 3

Function notation and relations

Maximal domains

Power functions and rules

Circles and their equations

Semicircles, regions and transformations

Line-circle contact

Rational models

Inverse relations and functions

Obtain the domain and range of a relation represented by ordered pairs, a table, a rule or described graph data, preserving set membership and open or closed endpoints

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RESTS ON

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Determine whether each input in a relation has exactly one output; on graph data, apply the vertical-line testForm a function's maximal real domain by excluding zeros of denominators, requiring radicands to be non-negative, requiring denominator radicands to be positive, and intersecting all component restrictionsIdentify 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 functionConstruct the inverse of a relation by interchanging every ordered pair, hence interchanging domain and range, and map graph points through reflection in y=xConnect a circle's centre, positive radius, centre–radius equation, extremal coordinates, domain and rangeIdentify growth or decay, horizontal asymptote, intercepts, domain, range, one-to-one status and end behaviour of a basic or transformed exponential graph CH 11Identify orientation, vertical asymptote, intercepts, domain, range, one-to-one status and end behaviour of a basic or transformed logarithmic graph CH 11Test the three continuity conditions at a stated input: the function value exists, the two-sided limit exists, and the two values agree CH 13Distinguish local extrema from global extrema and compare exact values at every admissible stationary input and included domain endpoint; decide when an unbounded domain has no global extremum CH 13