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?
first, draw the asymptotes. Then pick a few values of x near the vertical asymptotes, so you get a feel for how y behaves in that region.
Then pick a few more values a little farther away, and draw the curve, keeping in mind that it will approach the horizontal asymptote on the sides.
And watch out -- sometimes the graph will cross the horizontal asymptote and approach it from the other side. As with something like x/(x^2+1):
http://www.wolframalpha.com/input/?i=x%2F%28x^2%2B1%29
3(x+2)=3x+6
To graph the rational function y = 1/(x - 2) - 6, you can choose various values for x and then evaluate the corresponding y-values. Here's how you can determine which values to use:
1. Consider the domain: The domain of the function is all real numbers except x = 2 (since that would make the denominator zero, resulting in an undefined value). So, you can choose values for x that are slightly less than and greater than 2.
2. Identify any important points: In this case, we have two asymptotes (x = 2 and y = -6). These indicate key features of the graph and help us determine values to choose. We can choose values close to, but not equal to, these asymptotes.
3. Choose x-values and evaluate y-values: To get a good sense of the shape of the graph, select a range of x-values. For example, you can choose values such as -5, -3, 0, 1, 3, and 5. Plug each of these x-values into the function and calculate the corresponding y-values.
Once you have the x and y-values, you can plot the points on a graph and connect them to observe the shape and behavior of the rational function. Since we know the asymptotes, you can draw dashed lines to represent the vertical asymptote x = 2 and the horizontal asymptote y = -6.
Remember to label the axes of the graph appropriately and make sure to include any significant points determined by the chosen x-values (such as intercepts or other key points).
By following this method, you can choose values for graphing rational functions and visualize their behavior.