Exponential and Logarithmic Functions - Sketching Exponential Functions and Solving Equations Graphically
Exponential and Logarithmic Functions - Sketching Exponential Functions and Solving Equations Graphically
IP 3
The curve of \(y=a{{\mathrm{e}}^{2x}}-b\) passes through \(\left( \frac{1}{2},0 \right)\) and \(\left( 0,1-\mathrm{e} \right)\). Find the values of \(a\) and \(b\).
Hence, sketch the graphs of \(y=a{{\mathrm{e}}^{2x}}-b\), labelling the coordinates of axial intercepts and equations of asymptotes.
Solution:
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Answer:\(a=1\), \(b=\mathrm e\). Intercepts: \(\left(\dfrac12,0\right)\), \((0,1-\mathrm e)\). Horizontal asymptote: \(y=-\mathrm e\).
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