You are right. Misinterpreted.wabbit said:
A rational function is a mathematical function that can be expressed as the ratio of two polynomial functions. It is written in the form f(x) = p(x)/q(x), where p(x) and q(x) are polynomial functions and q(x) is not equal to 0.
To graph a rational function, first find the asymptotes by setting the denominator equal to 0 and solving for x. Then, plot these asymptotes on the graph. Next, find the x and y-intercepts by setting the numerator equal to 0 and solving for x. Finally, plot these points and any other points needed to complete the graph.
A vertical asymptote is a vertical line on the graph of a rational function where the function approaches positive or negative infinity. It occurs at values of x where the denominator of the function is equal to 0.
To simplify a rational function, factor both the numerator and denominator and then cancel out any common factors. This will result in a simplified form of the function that is easier to work with.
Calculus is used to study rational functions by analyzing their derivatives and integrals. The derivative of a rational function can provide information about the slope and concavity of the function, while the integral can be used to find the area under the curve. Additionally, calculus techniques such as finding limits and using the intermediate value theorem can be used to solve problems involving rational functions.