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 \(y={{a}^{3x+b}}+3\) passes through \(\left( 0,\frac{7}{2} \right)\) and \(\left( -\frac{2}{3},5 \right)\). Find the values of \(a\) and \(b\).

Hence, sketch the graphs of \(y={{a}^{3x+b}}+3\), labelling the coordinates of axial intercepts and equations of asymptotes.

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Answer:\(a = \dfrac{1}{2}\), \(b = 1\)

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