A function is defined by \(f(x)=\ln(x-2)\), where \(x\ne 2\). Sketch the graph of \(y=f(x)\), clearly indicating the asymptotes and intercepts. [2] Hence, sketch the graph of \(y=f(|x|)\) on a separate set of axes, clearly indicating any asymptotes and axial intercepts.[3]

Exponential and Logarithmic Functions - Sketching Logarithmic Functions and Solving Equations Graphically

5 marks

A function is defined by \(f(x)=\ln(x-2)\), where \(x\ne 2\).

Sketch the graph of \(y=f(x)\), clearly indicating the asymptotes and intercepts.
[2]
Hence, sketch the graph of \(y=f(|x|)\) on a separate set of axes, clearly indicating any asymptotes and axial intercepts.[3]

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Answer:(a) Vertical asymptote \(x=2\); \(x\)-intercept \((3,0)\); no \(y\)-intercept. (b) Vertical asymptotes \(x=\pm2\); \(x\)-intercepts \(\left(\pm3,0\right)\); no \(y\)-intercept.

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