It is no secret that math can be a difficult subject for many students. One of the most challenging concepts to master is rational functions, which can be confusing and difficult to graph. If you are stuck trying to determine which of the following rational functions is graphed below, fear not. Here is a guide to help you understand and identify the function.
What Is A Rational Function?
A rational function is a type of function where the expression which defines it is a ratio of two polynomials. A polynomial is an expression which contains one or more variables with non-negative integer exponents. The most common examples of rational functions are fractions, such as 2/3 or 5/7. When graphed, these functions typically appear as a curve or line.
Graphing Rational Functions
When graphing rational functions, it is important to identify the two components: the numerator and the denominator. The numerator is the part of the function that is on top, while the denominator is the part of the function that is on the bottom. Depending on the values of the numerator and denominator, the graph of the rational function can have different shapes. Knowing how to identify the shapes of a rational function graph is essential for determining which of the following rational functions is graphed below.
Types Of Rational Function Graphs
The graph of a rational function can take a few different forms, depending on the values of the numerator and denominator. The most common types of rational function graphs are the following:
- A horizontal line, if the numerator is equal to zero
- A vertical line, if the denominator is equal to zero
- A slanted line, if the numerator is greater than the denominator
- A curved line, if the numerator is less than the denominator
Identifying The Function Graphed Below
Once you have identified the type of graph, you can use the information to determine which of the following rational functions is graphed below. The type of graph will tell you the relationship between the numerator and the denominator. For example, if the graph is a slanted line, then the numerator is greater than the denominator. If the graph is a curved line, then the numerator is less than the denominator. By comparing the graph to the values of the numerator and denominator, you can determine which of the following rational functions is graphed below.
Conclusion
Graphing rational functions can be a difficult and confusing process. However, with a little bit of knowledge and practice, it is possible to determine which of the following rational functions is graphed below. By understanding the types of graphs that can be created and comparing the values of the numerator and denominator to the shape of the graph, you can successfully identify the function graphed below.
