How do you graph #y=3tan(1/2x)-2#?
As below.
graph{3 tan(x/2) - 2 [-10, 10, -5, 5]}
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To graph the function y = 3tan(1/2x) - 2, follow these steps:
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Identify the key characteristics of the tangent function: it has vertical asymptotes where the denominator becomes zero, and its period is π.
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Determine the vertical asymptotes by setting the denominator of the tangent function equal to zero: 1/2x = kπ, where k is an integer.
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Solve for x to find the locations of the vertical asymptotes.
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Plot these vertical asymptotes on the x-axis.
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Find the period of the function, which is π. This means that the function repeats every π units.
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Choose points to the left and right of each vertical asymptote, and calculate their y-values using the function.
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Plot these points on the graph.
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Connect the points smoothly to represent the graph of the function between each pair of vertical asymptotes.
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Note that the graph of the tangent function has a horizontal shift due to the coefficient 1/2 in the argument. This shift depends on the value of 1/2x.
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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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