Understanding Hyperbolic Functions

The video tutorial explains the graphs of hyperbolic functions, including hyperbolic sine, cosine, tangent, and their reciprocals. It covers the mathematical expressions, graphing techniques, and properties such as asymptotes and domain/range for each function. The tutorial emphasizes understanding the functions' behavior through their exponential components, aiding in memorization and application.

What is the formula for the hyperbolic sine function?

• e^x / e^(-x) / 2

• e^x * e^(-x) / 2

• e^x - e^(-x) / 2

• e^x + e^(-x) / 2

As x approaches positive infinity, what happens to the hyperbolic sine function?

• It approaches positive infinity

• It approaches negative infinity

• It remains constant

• It approaches zero

What is the domain of the hyperbolic cosecant function?

• Only positive numbers

• Only negative numbers

• All real numbers except zero

• All real numbers

How does the hyperbolic cosecant function behave as it approaches zero?

• It remains constant

• It approaches positive infinity

• It approaches zero

• It approaches negative infinity

What is the range of the hyperbolic cosine function?

• Negative one to positive infinity

• One to positive infinity

• Zero to positive infinity

• Negative infinity to positive infinity

What is the relationship between hyperbolic cosine and hyperbolic secant?

• They are identical

• They are reciprocals

• They are unrelated

• They are inverses

What is the range of the hyperbolic secant function?

• One to positive infinity

• Zero to one

• Zero to positive infinity

• Negative infinity to positive infinity

Which form is easiest to use for graphing the hyperbolic tangent function?

• e^(2x) - 1 / e^(2x) + 1

• e^x - e^(-x) / 2

• e^x + e^(-x) / 2

• e^x - e^(-x) / e^x + e^(-x)

What is the domain of the hyperbolic tangent function?

• All real numbers

• Only negative numbers

• All real numbers except zero

• Only positive numbers

How does the hyperbolic cotangent function behave as it approaches zero from the right?

• It remains constant

• It approaches negative infinity

• It approaches positive infinity

• It approaches zero