how to graph y= (x^2-3x-10)/(x-2)
(x-5)(x+2)/(x-2)
well we know it is 0 at x = 5 and at x = -2
and we know it explodes at x = 2
we know it goes to y = x as x gets +big
we know it goes to y = -x as x gets -big
now between those zeros at -2 and+5
lies x = 0 when y is 10/2 = 5
so that is a start :)
I don't understand what you mean "it is 0 at x=5 and at x=-2"?
To graph the function y = (x^2 - 3x - 10) / (x - 2), you can follow these steps:
1. Determine the x-intercepts of the function. Set the denominator equal to zero and solve for x: x - 2 = 0. Solving this equation yields x = 2. So, the function has a vertical asymptote at x = 2.
2. Determine the y-intercept by substituting x = 0 into the function. Calculating y when x = 0, we get y = (0^2 - 3(0) - 10) / (0 - 2) = -10 / -2 = 5. Therefore, the y-intercept is (0, 5).
3. Find any vertical asymptotes. Since we already found out that x = 2 is a vertical asymptote, we don't have any other vertical asymptotes for this function.
4. Plot additional points. Choose some x-values on either side of the vertical asymptote (x = 2) and find the corresponding y-values. For example, when x = 1, y = (1^2 - 3(1) - 10) / (1 - 2) = -12. So, we have the point (1, -12). Similarly, when x = 3, y = (3^2 - 3(3) - 10) / (3 - 2) = 2. Therefore, we have the point (3, 2).
5. Sketch the graph. Using the information gathered, sketch the graph of the function by connecting the points and showing the vertical asymptote. The graph should look like a hyperbola with a vertical asymptote at x = 2.
Note: Due to the complexity of the function, it may be helpful to use graphing software or an online graphing tool to visualize the graph more accurately and obtain additional points.