Find the horizontal and vertical asymptotes of the curve.

y = 3x+6/x−7

x=
y=

To find the horizontal and vertical asymptotes of a curve, we need to analyze the behavior of the function as x approaches positive or negative infinity.

Let's start by finding the horizontal asymptote. We look at the highest degree terms in the numerator and denominator of the function. In this case, the numerator is 3x+6 and the denominator is x-7. The degree of the numerator is 1, and the degree of the denominator is also 1. Since the degrees are the same, we divide the coefficients of the highest degree terms, which are 3 and 1. The result is 3/1 = 3.

Therefore, the horizontal asymptote of the curve is y = 3.

Next, let's find the vertical asymptote(s). To do this, we set the denominator equal to zero and solve for x. In this case, we have x - 7 = 0. Solving this equation, we find x = 7.

So, the vertical asymptote of the curve is x = 7.

To summarize:
Horizontal asymptote: y = 3
Vertical asymptote: x = 7

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