How do you graph and find the discontinuities of #1 /(x+6)#?
graph{1/(x+6) [10, 10, 5, 5]} and
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To graph and find the discontinuities of the function 1/(x+6), follow these steps:

Start by determining the vertical asymptote(s) of the function. Set the denominator (x+6) equal to zero and solve for x. In this case, x = 6 is the vertical asymptote.

Next, find the horizontal asymptote of the function. Since the degree of the numerator (which is 1) is less than the degree of the denominator (which is 1), the horizontal asymptote is y = 0.

Plot the vertical asymptote at x = 6 and the horizontal asymptote at y = 0 on the coordinate plane.

To graph the function, choose some xvalues on both sides of the vertical asymptote (6) and evaluate the corresponding yvalues using the function. Plot these points on the graph.

Connect the plotted points smoothly, approaching the vertical asymptote without crossing it.

The graph of 1/(x+6) will have a hole at x = 6 since the function is undefined at that point. Indicate this by leaving an open circle at the corresponding point on the graph.

The graph will approach the horizontal asymptote (y = 0) as x approaches positive or negative infinity.
This completes the process of graphing and identifying the discontinuity of the function 1/(x+6).
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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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