How do you graph #y=1/[x(x2)]#?
To graph the function y=1/[x(x2)], we can follow these steps:

Determine the domain of the function by identifying the values of x that make the denominator zero. In this case, x cannot be equal to 0 or 2.

Find the vertical asymptotes by setting the denominator equal to zero and solving for x. In this case, x=0 and x=2 are the vertical asymptotes.

Determine the behavior of the function as x approaches positive and negative infinity. As x approaches positive or negative infinity, the function approaches zero.

Find the xintercepts by setting y equal to zero and solving for x. In this case, there are no xintercepts.

Determine the yintercept by substituting x=0 into the equation. In this case, the yintercept is (0, 1/0).

Plot the vertical asymptotes, xintercepts (if any), and the yintercept on the coordinate plane.

Choose additional xvalues to evaluate the function and plot the corresponding points on the graph.

Connect the plotted points smoothly to form the graph.
Remember to label the axes and provide a title for the graph.
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You find the intercepts and the asymptotes, and then you sketch the graph.
Step 1. Find the
There is no
Step 2. Find the
There is no
Step 3. Find the vertical asymptotes.
Set the denominator equal to zero and solve for
There are vertical asymptotes at
Step 4. Find the horizontal asymptote.
The degree of the denominator is greater than the degree of the numerator, so
The horizontal asymptote is at
Step 5. Draw your axes and the asymptotes.
The vertical asymptotes divide the graph into three regions of
(a) The left hand region has the
The point at (
(b) The right hand region has
The point at (
So we have a mirrorimage hyperbola in the first quadrant.
(c) In the middle region, we have
The points at (
And we have our graph.
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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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