11–12Mathematics Extension 1 11–12 Syllabus

Determine the domains and ranges of the sum and difference of functions where possible, and, if appropriate, verify them using a graphing application

Apply knowledge of graphical relationships to solve problems involving graphs of functions, justifying conclusions in the context of the problem where appropriate

Describe a function as one-to-one if every element in the range of the function corresponds to exactly one element of the domain

Recognise that inverse functions exist for one-to-one functions

Graph the inverse function of a given one-to-one function

Apply restrictions to the domain of a function, if it is not one-to-one, to obtain an inverse function

Solve problems based on the relationship between a function and its inverse function using algebraic and graphical techniques, including determining the points of intersection of a function and its inverse, where they exist

Express linear and quadratic functions and circles in parametric form

Convert linear and quadratic functions and circles from parametric form to Cartesian form

Graph linear and quadratic functions and circles expressed in parametric form

Solve cubic inequalities where the cubic is expressed as a product of linear factors

Solve inequalities involving rational expressions with variables in the denominator