Which Of The Following Rational Functions Is Graphed Below?

In 2023, the subject of mathematics is still a major area of focus for many students. One of the most popular topics of study is rational functions, which refer to equations that have fractions in their denominator. In some instances, it is necessary to graph a rational function to help solve a problem. This article will look at the question of which of the following rational functions is graphed below.

What Are Rational Functions?

Rational functions are equations that contain fractions in the denominator. These equations can take on many forms, but in general, they all share the property of having a fraction in the denominator. For instance, one common form of a rational function is y = (x+2)/(x-3). In this equation, the denominator is a fraction, consisting of a single variable (x) and a scalar (3). Rational functions are often used to solve a variety of problems in mathematics. They can be used to find the roots of an equation, to solve for a particular variable, or to graph a particular equation.

Graphing Rational Functions

Graphing a rational function begins with finding the zeroes of the equation. To do this, the numerator and denominator of the equation are set equal to zero. This will give two equations that can be solved for the zeroes. Once the zeroes are found, it is then possible to graph the equation. When graphing a rational function, it is important to note that the graph will have asymptotes. An asymptote of a graph is a line that the graph approaches but never crosses. This line is usually referred to as a "horizontal asymptote" or a "vertical asymptote," depending on its orientation.

Which of the Following Rational Functions is Graphed Below?

When looking at a graph of a rational function, it can be difficult to determine which equation it is. This is because the graph of a rational function looks very similar to the graph of other types of equations. In order to identify which of the following rational functions is graphed below, it is important to look for certain features. These features include the number of zeroes, the asymptotes, and the general shape of the graph. By looking for these features, it is often possible to narrow down the possibilities and identify the correct equation.

Identifying Zeroes

The first step in identifying which of the following rational functions is graphed below is to identify the zeroes of the equation. This can be done by looking for the points on the graph where the line crosses the x-axis. These points indicate that the equation has a zero at that point, and can help to narrow down the possibilities.

Identifying Asymptotes

The next step in identifying which of the following rational functions is graphed below is to look for the asymptotes. Asymptotes are lines that the graph approaches but never crosses. They are usually referred to as horizontal or vertical asymptotes, depending on their orientation. By looking for these lines, it is often possible to narrow down the possibilities and identify the correct equation.

Identifying the Shape of the Graph

The final step in identifying which of the following rational functions is graphed below is to look for the general shape of the graph. By looking for certain features, such as the number of peaks and valleys, it is often possible to narrow down the possibilities and identify the correct equation.

Conclusion

Identifying which of the following rational functions is graphed below is an important skill for any math student to possess. By looking for certain features, such as zeroes, asymptotes, and the general shape of the graph, it is often possible to narrow down the possibilities and identify the correct equation. By understanding the techniques discussed in this article, any student should be able to solve this type of problem with ease.