The global behavior of rational functions depends on the degree of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the function will have a horizontal asymptote at y=0. If the degree of the numerator is equal to the degree of the denominator, the function will have a horizontal asymptote at the ratio of the leading coefficients. If the degree of the numerator is greater than the degree of the denominator, the function will have a slant or oblique asymptote. Additionally, rational functions may have vertical asymptotes where the denominator is equal to zero. Overall, the global behavior of rational functions is determined by the relationship between the degrees of the numerator and denominator. **

Yes, the product of two rational numbers is also rational. This is because when you multiply two rational numbers, the result can always be expressed as a ratio of two integers, which is the definition of a rational number. Therefore, the product of two rational numbers will always be rational. **

One can determine the global behavior of rational functions computationally by analyzing the function's behavior at its critical points, asymptotes, and end behavior. This can be done by finding the function's derivative and setting it equal to zero to find critical points, and by analyzing the function's behavior near its vertical and horizontal asymptotes. Additionally, one can use computational tools such as graphing calculators or computer software to graph the function and observe its behavior over its entire domain. By analyzing these key points and using computational tools, one can determine the global behavior of rational functions. **

Yes, the product of rational numbers is also a rational number. This is because when you multiply two rational numbers, the result can always be expressed as a fraction of two integers, where the denominator is not zero. Therefore, the product of rational numbers is always a rational number. **

When calculating the global behavior of rational functions, it is important to consider the degree of the numerator and denominator polynomials. The behavior at the vertical asymptotes, horizontal asymptotes, and x-intercepts should also be taken into account. Additionally, the end behavior as x approaches positive or negative infinity should be analyzed to determine the overall shape of the graph. Finally, any holes or removable discontinuities in the function should be identified and considered in the overall behavior analysis. **

Rational functions are functions that can be expressed as the ratio of two polynomials. They are defined for all real numbers except where the denominator polynomial is equal to zero. Rational functions can have vertical asymptotes where the denominator is zero, and horizontal asymptotes as x approaches positive or negative infinity. These functions can have a variety of shapes and behaviors depending on the degree of the numerator and denominator polynomials. **

Man is still rational to a certain extent, as humans have the ability to think critically, make decisions based on logic and reason, and solve complex problems. However, emotions, biases, and external influences can sometimes cloud our judgment and lead to irrational behavior. It is important for individuals to be aware of these factors and strive to make rational decisions based on sound reasoning and evidence. **

People are generally considered to be rational to some extent, as they are capable of making logical decisions based on their beliefs, preferences, and available information. However, human behavior is also influenced by emotions, biases, and cognitive limitations, which can lead to irrational decision-making. While people strive to be rational, they are also subject to various psychological and social factors that can impact their ability to make purely rational choices. Overall, people can be rational in certain situations, but their decision-making is often influenced by a combination of rational and irrational factors. **