NSW Y11 Maths - Extension 1 Functions Absolute Value Functions

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Given the graph \(y = f(x)\) the graphs of \(y = \left| {f(x)} \right|\) or \(y = f\left( {\left| x \right|} \right)\) are the absolute value functions.

For example, if \(y = x + a\), \(y = \left| {f(x)} \right|\)\( \to y = \left| {x + a} \right|\), \(y = f\left( {\left| x \right|} \right)\)\( \to y = \left| x \right| + a\)

NSW Syllabus Reference: ME-F1.1: Graphical relationships. This will require student to 

• examine the relationship between the graph of \(y=f(x)\) and the graph of \(y=\dfrac{1}{f(x)}\) and hence sketch the graphs (ACMSM099)
• examine the relationship between the graph of \(y=f(x)\) and the graphs of \(y^2=f(x)\) and \(y=\sqrt{f(x)}\) and hence sketch the graphs
• examine the relationship between the graph of \(y=f(x)\) and the graphs of \(y=|f(x)|\) and \(y=f(x)+g(x)\) and hence sketch the graphs (ACMSM099)
• examine the relationship between the graphs of \(y=f(x)\) and \(y=g(x)\) and the graphs of \(y=f(x)+g(x)\) and \(y=f(x)g(x)\) and hence sketch the graphs
• apply knowledge of graphical relationships to solve problems in practical and abstract contexts

Ref: https://educationstandards.nsw.edu.au/