How do you graph #f(x) = (2x^2 + x - 3) / (2x^2 - 7x)#?

To graph the function f(x) = (2x^2 + x - 3) / (2x^2 - 7x), follow these steps:

1. Determine the domain of the function by finding the values of x for which the denominator is equal to zero. In this case, set the denominator (2x^2 - 7x) equal to zero and solve for x. The solutions will give you the values to exclude from the domain.

2. Simplify the function if possible. In this case, the function cannot be simplified further.

3. Find the y-intercept by substituting x = 0 into the function and solving for y.

4. Determine the vertical asymptotes by setting the denominator equal to zero and solving for x. These values will give you the vertical lines that the graph approaches but never touches.

5. Determine the horizontal asymptotes by comparing the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If the degrees are equal, divide the leading coefficients of the numerator and denominator to find the horizontal asymptote.

6. Plot additional points by choosing various x-values and calculating the corresponding y-values using the function.

7. Use the information gathered to sketch the graph, connecting the points and approaching the asymptotes as appropriate.

Please note that without specific values for x, it is not possible to provide an accurate graph.

To graph the function ( f(x) = \frac{2x^2 + x - 3}{2x^2 - 7x} ), you can follow these steps:

1. Factor the numerator and denominator.
2. Identify any vertical asymptotes where the denominator equals zero.
3. Determine any horizontal asymptotes.
4. Find the x-intercepts and y-intercepts.
5. Choose additional points to plot the graph.
6. Sketch the graph using the information gathered from steps 2-5.