Working with Functions

Function notation, domain, range, roots, intercepts, linear, quadratic, cubic, polynomial, and reciprocal graph features.

Active lessons

Status

Active

Lesson flow

Learn -> Guided Practice -> Independent Practice -> Mastery Quiz

How to use this unit

Start from lesson 1 and move through the pathway in order.
Use guided practice before attempting independent practice.
Mastery quizzes check whether the skill is ready for review or extension.

Unit pathway

Lesson pathway

16 of 16 active

Lesson 1

Function Notation, Domain and Range

Evaluate functions, handle negative inputs, and identify domain and range restrictions from rules, tables and graph descriptions.

Lesson 2

Linear, Quadratic and Cubic Functions

Compare linear, quadratic and cubic functions using intercepts, roots, turning points, tables and graph descriptions.

Lesson 3

Polynomial and Reciprocal Functions

Use degree, leading coefficient, roots, factors, reciprocal functions and asymptotes to interpret function features.

Lesson 4

Absolute Value Functions

Evaluate, sketch and interpret absolute-value functions, including transformations of y = |x|.

Lesson 5

Odd and Even Functions

Classify functions as even, odd or neither using f(-x) tests and graph symmetry.

Lesson 6

Apply index laws to positive, negative, zero and fractional indices; expand, factorise and simplify algebraic expressions; simplify algebraic fractions; expand and simplify surds; rationalise denominators of the form 1/(√a ± √b).

Lesson 7

Quadratic Equations and the Discriminant

Solve quadratic equations by factorisation, completing the square and the quadratic formula; define and evaluate the discriminant; use conditions on the discriminant to determine the nature of roots.

Lesson 8

Linear Functions

Use gradient-intercept, general and point-gradient forms; find x- and y-intercepts; graph linear functions; identify parallel and perpendicular relationships; solve and graph linear inequalities.

Lesson 9

Constructing and Using Functions

Construct and use linear and quadratic functions as models; apply linear inequalities in context; solve simultaneous linear equations; interpret cost-revenue and break-even problems.

Lesson 10

Direct and Inverse Variation

Model direct variation y = kx and inverse variation y = k/x; evaluate the constant of variation; use the model to find unknown values.

Lesson 11

Circles and Semicircles

Derive x² + y² = r² using the distance formula; graph circles centred at the origin; identify and graph semicircles y = ±√(r² − x²).

Lesson 12

Piecewise-Defined Functions

Interpret and graph piecewise-defined functions; determine domain, range and continuity; test for even or odd symmetry in piecewise rules.

Lesson 13

Composite Functions

Form and evaluate composite functions f∘g; distinguish (f∘g)(x) from (g∘f)(x); determine the domain of composite functions.

Lesson 14

Completing the Square

Rewrite quadratics in vertex form a(x − h)² + k; identify the vertex and axis of symmetry; solve quadratic equations by completing the square.

Lesson 15

Quadratic Inequalities

Solve quadratic inequalities by finding roots and using the parabola's sign above and below the x-axis; express solutions using interval notation.

Lesson 16