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What is the horizontal asymptote of the function f(x)=2x−5?

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Final answer:

The function f(x) = 2x - 5 is a linear function and does not have a horizontal asymptote because its graph is a straight line that continues to increase or decrease without leveling off.

Step-by-step explanation:

The question is asking about the horizontal asymptote of the function f(x) = 2x - 5. A horizontal asymptote of a function is a horizontal line that the graph of the function approaches but does not cross as x tends towards positive or negative infinity. The function given is a linear function, which means its graph is a straight line. Since the function is linear and not a fraction where the degree of the polynomial in the numerator is less than or equal to the polynomial in the denominator, it does not have a horizontal asymptote. Instead, the line just keeps increasing or decreasing without leveling off. However, we can consider what happens to the value of f(x) as x increases or decreases without bounds. As x goes to infinity, f(x) also goes to infinity, and as x goes to negative infinity, f(x) goes to negative infinity. Therefore, since the graph of f(x) does not approach any particular horizontal line, there is no horizontal asymptote for this function.

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