Rational functions are functions that can be expressed as a ratio of two polynomials. Graphing rational functions can be a challenging task, as they often have vertical asymptotes, horizontal asymptotes, and holes in their graphs. To help students practice graphing these types of functions, teachers often provide worksheets that contain various rational functions to graph.
Graphing rational functions worksheets typically include a variety of problems that require students to identify the vertical and horizontal asymptotes, any holes in the graph, and the behavior of the function as x approaches positive and negative infinity. Students are also often asked to sketch the graph of the function based on these characteristics.
One common type of problem found on graphing rational functions worksheets is determining the vertical asymptotes of the function. Vertical asymptotes occur when the denominator of the rational function is equal to zero, leading to a division by zero error. Students must identify where these vertical asymptotes occur and draw them on the graph.
Another type of problem found on these worksheets is determining the horizontal asymptotes of the function. Horizontal asymptotes occur when the degree of the numerator and denominator polynomials are equal. Students must analyze the leading coefficients of the polynomials to determine the horizontal asymptotes and sketch them on the graph.
Additionally, students may be asked to identify any holes in the graph of the rational function. Holes occur when factors in the numerator and denominator of the function cancel out, resulting in a gap in the graph. Students must locate these holes and accurately sketch the graph around them.
In conclusion, graphing rational functions worksheets are valuable tools for students to practice identifying and graphing the key features of rational functions, such as vertical and horizontal asymptotes and holes. By working through these worksheets, students can strengthen their understanding of rational functions and improve their graphing skills.