How do you graph #y=3 + 2/(4−x)#?
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To graph the equation y = 3 + 2/(4  x), you can follow these steps:

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.

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

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

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

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.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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