Question

which of the following are the same for both the tangent and cotangent functions? domain range asymptotes period intercepts

Answer 1

The domain of both the tangent and cotangent functions is all real numbers except where the function is undefined. The range of both functions is all real numbers. Both functions have asymptotes and a period of pi, and they do not have intercepts.

Step-by-step explanation:

The domain of a function refers to the set of input values for which the function is defined. For both the tangent and cotangent functions, the domain is all real numbers except for the values where the function is undefined, which occur when the denominator of the function is zero.The range of a function refers to the set of output values that the function can produce. For both the tangent and cotangent functions, the range is all real numbers.The asymptotes of a function are lines that the graph of the function approaches but never crosses. The tangent and cotangent functions have asymptotes at regular intervals along their graphs. The tangent function has vertical asymptotes at odd multiples of pi/2, while the cotangent function has vertical asymptotes at multiples of pi.The period of a function refers to the length of one complete cycle of the function. The tangent and cotangent functions have a period of pi.The intercepts of a function refer to the points where the graph of the function crosses the x-axis and the y-axis. Since both the tangent and cotangent functions are periodic and have asymptotes, they do not cross the x-axis or the y-axis, so they do not have intercepts.

Answer 2

Domain and period are the same for both tangent and cotangent functions.

First, we need to know the following;

The tangent function has vertical asymptotes and the cotangent function has value 0 and vice versa.

Period: The period of the tangent function is π (periodicity every π units). The period of the cotangent function is also π.

Intercepts: Both tangent and cotangent functions have intercepts, but they occur at different points on the coordinate plane due to their different behaviors.

Thus, the domain and period are the same for both tangent and cotangent functions, while their range, asymptotes, and intercepts differ.