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What is the domain of the function tangent of negative 𝜋𝑥 over two whose graph is shown?
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The domain will be all of the 𝑥-values that the graph represents.
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So essentially, we have to ask ourselves, is there anywhere on the 𝑥-axis that a number doesn’t have somewhere to actually land?
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So almost every value on our 𝑥-axis has a place to go, and it’s represented by that arrow.
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So, for example, at zero, at 𝑥 equals zero, 𝑦 is equal to zero.
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And at 𝑥 is a positive small, small fraction, we end up below the 𝑥-axis for negative four 𝑦, and it decreases as we get closer and closer to one.
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However, at one, we actually can’t land anywhere where 𝑥 equals one; that is called an asymptote, and it’s a value that the graph will approach but never actually reach.
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So 𝑥 equals one we’ll never reach, 𝑥 equals three we won’t reach, 𝑥 equals negative one, and 𝑥 equals negative three.
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So all of the 𝑥-values except for these will work.
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So our domain will be all real numbers except these specific values, so how do we classify these?
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Well it’s not just the integers because it doesn’t include two or zero or negative two or negative four; it excludes all of those even integers, so this must be the odd integers.
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So our domain must be all real numbers except odd integers.