How do you graph #y=1/[x(x-2)]#?
To graph the function y=1/[x(x-2)], we can follow these steps:
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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.
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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.
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Determine the behavior of the function as x approaches positive and negative infinity. As x approaches positive or negative infinity, the function approaches zero.
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Find the x-intercepts by setting y equal to zero and solving for x. In this case, there are no x-intercepts.
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Determine the y-intercept by substituting x=0 into the equation. In this case, the y-intercept is (0, -1/0).
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Plot the vertical asymptotes, x-intercepts (if any), and the y-intercept on the coordinate plane.
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Choose additional x-values to evaluate the function and plot the corresponding points on the graph.
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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 mirror-image 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 one-sided 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 one-sided 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 one-sided 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 one-sided 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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