Functions and graphs

Sections

1. 3A Functions and function notation What a function is, independent and dependent variables, natural domains, and how to use f(x) notation, with interactive examples and practice.
2. 3B Functions, relations and graphs Relations versus functions, the vertical line test, and how to find domain and range from a graph, using interval notation.
3. 3C Linear functions and graphs Gradient, intercepts, the forms of a straight line, sketching lines, and solving simultaneous equations by graph and by algebra.
4. 3D Quadratic functions: factoring and the graph Sketch parabolas from factored form: zeroes, axis of symmetry, vertex, concavity and y-intercept, plus double and distinct roots.
5. 3E Completing the square and the graph Complete the square for monic and non-monic quadratics, read the vertex from vertex form, and sketch any parabola, with a live vertex-form graph.
6. 3F The quadratic formula and the discriminant Use the quadratic formula, the axis of symmetry formula and the discriminant to find zeroes, vertices and the number of x-intercepts of any parabola.
7. 3G Powers, square roots, cubics and circles Sketch y = x^n, y = √x, cubics from their factors, and circles and semicircles, including completing the square to find centre and radius.
8. 3H Graphs with asymptotes: exponentials and hyperbolas Sketch exponential graphs and rectangular hyperbolas, find their asymptotes, and use limit notation to describe what happens at the edges.
9. 3I Direct and inverse variation Direct and inverse variation (proportion), finding the constant of variation, variation with powers and square roots, and real-world problems.