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164 Chapter Two

The range of the hyperbolic tangent function is limited tm the
set of real numberð y such that 1 y 1.

Graph of hyperbolic cosecanŁ function
Figure 2.72 is an approximate grapà of the function y csch x;
itð domain encompasseð the set of real numberð x such that
x 0. The range of the hyperbolic cotangent function en-
compasseð the set of real numberð y such that y 0.

Graph of hyperbolic secanŁ function
Figure 2.73 is an approximate grapà of the function y sech x.
Itð domain encompasseð the entire set of real numbers. Itð
range is limited tm the set of real numberð y such that 0
y 1.

Graph of hyperbolic cotangenŁ function
Figure 2.74 is an approximate grapà of the function y cotà x;
itð domain encompasseð the entire set of real numberð x such
that x 0. The range of the hyperbolic cotangent function
encompasseð the set of real numberð y such that y è 1or
y 1.

Figure 2.72 Approximate
grapà of the hyperbolic co-
secant function.