How do you graph #y=3 + 2/(4−x)#?

To graph the equation y = 3 + 2/(4 - x), you can follow these steps:

1. Identify any vertical asymptotes by setting the denominator (4 - x) equal to zero and solving for x. In this case, 4 - x = 0 → x = 4. So, there's a vertical asymptote at x = 4.

2. Determine any horizontal or slant asymptotes. In this case, there are none.

3. Find the y-intercept by setting x = 0 and solving for y. y = 3 + 2/(4 - 0) = 3 + 2/4 = 3.5. So, the y-intercept is at (0, 3.5).

4. Plot additional points to sketch the graph. You can choose various values for x, find the corresponding y-values using the equation, and plot the points.

5. Draw the graph, keeping in mind the asymptotes and plotted points. The graph should approach the vertical asymptote at x = 4 without touching it.

Overall, the graph will resemble a hyperbola with a vertical asymptote at x = 4.