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Maths Advanced

Solving Cubic Function Problems

How do I approach solving and graphing cubic function problems?

In this post, we learn to recognise cubic functions of the form: f(x) = x^{3}, f(x) = k(x - b)^{3} + c and f(x) = k(x - a)(x - b)(x - c), where a, b, c and k are constants, from their equation and/or graph and identify important features of the graph. This is part of the Prelim Maths Advanced course under the topic Working with Functions and sub-part Linear, Quadratic and Cubic Functions, specifically focussing on solving cubic function problems.

 

How do I graph cubic functions?

The following four videos cover the step-by-step methodical process to understand and graph cubics in various forms and recognise the respective graphical properties.

Part 1: Considering f(x) = x^{3}

 

Part 2: Vertical Translation f(x) = k(x - b)^{3} + c

 

Part 3: Factored form f(x) = k(x - a)(x - b)(x - c),

 

Part 4: Geometric Features