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What is the horizontal asymptote for the given function v=2-9?

The horizontal asymptote of a function is typically determined by the behavior of the function as it approaches positive or negative infinity. In this case, the function v = 2 - 9 is a constant function with a value of -7. Since it's a constant, it doesn't approach any specific value as x goes to infinity. Therefore, there is no horizontal asymptote for this function.

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Final answer:

The function v = 2 - 9, which simplifies to v = -7, is a constant function, and therefore it does not have a horizontal asymptote. Constant functions are represented by a horizontal line, and the value of v remains constant irrespective of x.

Step-by-step explanation:

The question is about finding the horizontal asymptote for the given function v = 2 - 9. In this case, this function simplifies to v = -7, which is a constant function. A constant function has a graph that is a horizontal line, and thus it does not have a horizontal asymptote in the typical sense because horizontal asymptotes describe the behavior of a function as it approaches infinity. The function value of v = -7 will remain the same irrespective of the value of x.

Looking at Figure A1 Slope and the Algebra of Straight Lines, which describes lines with a slope (m) and y-intercept (b), we see that these values determine the shape of a line. However, in the context of our function, since it's a constant function, there is no change in v for any change in x; therefore, the concept of slope doesn't apply here.

Asymptotes are usually associated with functions that have variables that increase or decrease without bound. In contrast, a horizontal line represented by our function has a constant y-value and does not exhibit this behavior. Therefore, it is more appropriate to simply state that our function is represented by a horizontal line at v = -7, rather than discussing it in terms of horizontal asymptotes.

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