Long description: workbook6block2fig1

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The image displays the graphs of the hyperbolic sine function, \text{sinh}(x), and the hyperbolic cosine function, \text{cosh}(x), plotted on a Cartesian coordinate system.

Alt text: The image displays the graphs of the hyperbolic sine function, \text{sinh}(x), and the hyperbolic cosine function, \text{cosh}(x), plotted on a Cartesian coordinate system.

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  • The graph shows two curves plotted on an x-y coordinate system.
  • One curve, labeled \text{sinh}(x), is a steep, upward-opening curve that passes through the origin and increases as \(x\) increases in both the positive and negative directions.
  • The second curve, labeled \text{cosh}(x), is a U-shaped curve that opens upward, with its vertex located at the origin (0, 1). It decreases as \(x\) moves away from the origin in either direction before increasing again.
  • Dashed lines represent the general shapes of the exponential functions, \(e^{-x}\) and \(e^{x}\), which are related to the hyperbolic functions shown.

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