Quadratics x=q
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Dr.Peterson
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The vertical asymptote is at x=q because that value would make the denominator zero.
The horizontal asymptote can be explained in different ways, so you should look at how your textbook explained it. Some just declare that, when the degrees of numerator and denominator are the same, the asymptote occurs when y equals the ratio of leading terms, which here is 3/1.
One explanation for that is that if you divide numerator and denominator by the largest power of x (here [MATH]x^1[/MATH]), you get [MATH]\frac{3x}{x-q} = \frac{3}{1-\frac{q}{x}}[/MATH], which approaches [MATH]\frac{3}{1}[/MATH] as x becomes very large.
The horizontal asymptote can be explained in different ways, so you should look at how your textbook explained it. Some just declare that, when the degrees of numerator and denominator are the same, the asymptote occurs when y equals the ratio of leading terms, which here is 3/1.
One explanation for that is that if you divide numerator and denominator by the largest power of x (here [MATH]x^1[/MATH]), you get [MATH]\frac{3x}{x-q} = \frac{3}{1-\frac{q}{x}}[/MATH], which approaches [MATH]\frac{3}{1}[/MATH] as x becomes very large.