Part 3/7:
The standard representation of the hyperbolic sine function entails plotting the equation ( \sinh(x) = \frac{e^x - e^{-x}}{2} ). The resulting graph displays an asymptotic behavior, gradually approaching zero. The graph will resemble a curve bending upward, confirming the function’s characteristics.
When we reflect this graph along the line ( y = x ) to obtain the inverse, we ensure this reflected curve maintains its one-to-one characteristic—leading us to the graph of ( \text{arc}\sinh(x) ).