NSW Y11 Maths - Extension 1 Functions Square Root Functions

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Given the graph \(y = f(x)\) the graph of \(y = \sqrt {f(x)} \) is the square root function.

The domain of this function is values of \(x\) for which \(f(x) \ge 0\).

The range for \(y = \sqrt {f(x)} \) is \(y \ge 0\) and the range for \(y = - \sqrt {f(x)} \) is \(y \le 0\).

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/