This is part of the HSC Mathematics Advanced course under the topic Functions and sub-part Solving Problems Graphically

In this post, we use graphical methods with supporting algebraic working to solve a variety of practical problems involving any of the functions within the scope of this syllabus, in both real-life and abstract contexts:

- Select and use an appropriate method to graph a given function, including finding intercepts, considering the sign of f(x) and using symmetry
- Determine asymptotes and discontinuities where appropriate (vertical and horizontal asymptotes only)
- Determine the number of solutions of an equation by considering appropriate graphs
- Solve linear and quadratic inequalities by sketching appropriate graphs

Here, we will have a look at an example of a parabola inequality problem, solving using algebraic and graphical methods.

Here, we will have a look at an example of a square root and reciprocal problem, solving using algebraic and graphical methods, and finding asymptotes and discontinuities.

Here, we will have a look at an example of a piecewise function problem, solving using algebraic and graphical methods, and selecting appropriate methods to graph a given function.

Here, we will have a look at an example of a cubic inequality problem, solving using algebraic and graphical methods, finding intercepts, considering the sign of f(x) , and using symmetry.

Here, we will have a look at an example of an inequality problem with x in the denominator, solving using algebraic and graphical methods, determining asymptotes and discontinuities where possible.