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For what value of π does this equation, two π₯ plus five over π₯ minus three equals π, have no solutions?
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The place where π would have no solutions would be the horizontal asymptote of this function.
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To find the horizontal asymptotes of a rational function, we have to consider the degree of the polynomials in the numerator and the denominator.
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If both polynomials are the same degree, divide the coefficient of the highest-degree terms.
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That definition has a lot of vocabulary words, so letβs walk slowly through it.
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First, it says if both polynomials β that means the polynomial in the numerator and the polynomial in the denominator β have the same degree; the degree of the polynomial is the highest degree of all of the terms.
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Our numerator has a degree of one because we only have π₯ to the first power.
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Our denominator also has a degree of one.
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The numerator and the denominator here have the same degree.
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Because thatβs true, our definition tells us divide the coefficient of the highest-degree terms.
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In the numerator, two is the highest coefficient of the degree of terms, and in the denominator, one is the highest coefficient.
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All we need to say to find the asymptote, to find the place, where thereβs no solution is divide two by one.
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When π equals two, this equation has no solutions.