Long description: workbook6block1fig2

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A graph showing the exponential function \(y=e^x\) plotted on a standard Cartesian coordinate system.

Alt text: A graph showing the exponential function \(y=e^x\) plotted on a standard Cartesian coordinate system.

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  • The image displays a standard two-dimensional Cartesian coordinate system with a horizontal axis labeled \(x\) and a vertical axis labeled \(y\).
  • A smooth, upward-curving line represents the function \(y=e^x\).
  • The curve passes through the point where \(x=0\) and \(y=1\), as indicated by the label '1' on the vertical axis intersecting the graph at this point.
  • As the value of \(x\) increases (moves to the right), the value of \(y\) increases rapidly, showing exponential growth.
  • As the value of \(x\) decreases (moves to the left), the curve approaches the horizontal axis but never touches or crosses it, indicating a horizontal asymptote at \(y=0\) for negative \(x\) values.

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