Hyperbolic Functions and Their Inverses

This video tutorial explains how to graph inverse hyperbolic functions by reflecting their regular counterparts across the line Y equals X. It covers the inverse hyperbolic sine, cosine, tangent, cosecant, secant, and cotangent functions, discussing their domains, ranges, and asymptotes. The tutorial emphasizes the importance of understanding the relationship between the original and inverse functions, including how domains and ranges are interchanged.

What is the key transformation needed to graph the inverse of a hyperbolic function?

• Translate the graph upwards

• Scale the graph horizontally

• Reflect the graph across the line Y = X

• Rotate the graph 90 degrees

When graphing the inverse hyperbolic sine function, what happens to the domain of the original function?

• It becomes the range of the inverse function

• It remains unchanged

• It becomes the domain of the inverse function

• It is halved

Why is the graph of the inverse hyperbolic cosine function restricted to one side?

• To make it pass the horizontal line test

• To make it pass the vertical line test

• To match the original function

• To simplify the graph

What is the minimum value of the hyperbolic cosine function?

• 0

• Infinity

• -1

• 1

In the inverse hyperbolic tangent function, what do the horizontal asymptotes become?

• Horizontal asymptotes

• No asymptotes

• Vertical asymptotes

• Diagonal asymptotes

What is the range of the inverse hyperbolic tangent function?

• All real numbers

• -Infinity to Infinity

• 0 to 1

• -1 to 1

Why do the hyperbolic cosecant and its inverse share the same shape?

• They have the same domain

• They are both linear

• They have the same range

• Their asymptotes are symmetric

What is the domain of the hyperbolic cosecant function?

• All real numbers

• -1 to 1

• 0 to Infinity

• Negative Infinity to zero Union zero to Infinity

What happens to the vertical asymptote of the hyperbolic cotangent function when graphing its inverse?

• It becomes a horizontal asymptote

• It becomes a diagonal asymptote

• It remains a vertical asymptote

• It disappears

What is the range of the inverse hyperbolic secant function?

• 0 to Infinity

• -1 to 1

• 0 to 1

• -Infinity to Infinity