HSC Together Year 12 Maths Advanced: Solving Problems Graphically

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# Solving Problems Graphically

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.

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