Which values should I use to graph the rational function y = 1/x-2 - 6? (The asymptotes are x = 2; y = -6.)
Also, what method could I use to choose values for graphing rational functions?
what about x=1, 10, -1, -10
To graph the rational function y = 1/(x-2) - 6, you can use a variety of values for x to find corresponding values for y. Here's how you can do it:
1. Start by choosing values for x that are different on both sides of the asymptote x = 2. For example, you can choose x values such as -1, 0, 1, 3, and 4.
2. Substitute each of these x values into the given equation and calculate the corresponding y values. For example, when x = -1, y = 1/(-1-2) - 6 = -1/3 - 6 = -6 1/3. Repeat this process for each x value you chose.
3. Plot the points (x, y) on a graph, where y is the corresponding value you calculated in the previous step for each x value. Connect the points smoothly to form a curve. In this case, you would have two separate curves, one on each side of the vertical asymptote at x = 2.
4. You can also include the asymptotes x = 2 and y = -6 as dashed lines to indicate their presence on the graph.
The method to choose values for graphing rational functions, as described above, is a commonly used approach. By selecting various x values that span the domain of the function and evaluating the corresponding y values, you can plot those points on a graph and connect them to visualize the shape of the function. Additionally, you should consider any relevant asymptotes and critical points while choosing your values for a more accurate depiction of the graph.