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

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

IP 3

Sketch \(y=3-{{\mathrm{e}}^{2x}}\). Find the equation of the straight line which must be drawn to solve the equation \(6-2{{\mathrm{e}}^{2x}}=x\).

Solution:

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Answer:Intercepts \((0,2)\), \(\left(\dfrac{\ln3}{2},0\right)\); horizontal asymptote \(y=3\). Required line: \(y=\dfrac x2\).

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