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Consider the following curve: y = x - 1/x. What is the equation of the curve?

User Kaesha
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Final answer:

The equation 'y = x - 1/x' represents a hyperbola, which includes the line term 'x' and the hyperbolic term '-1/x'. This curve approaches the x-axis and y-axis but never touches them, indicating they are asymptotes.

Step-by-step explanation:

The equation given by the student is y = x - 1/x. This is already the equation of the curve and it represents a hyperbola. The equation consists of a linear term x, which depicts a straight line, and a term -1/x representing the hyperbola part of the curve. When graphed, this equation will produce a curve that will approach but never touch the x-axis (horizontal asymptote) and the y-axis (vertical asymptote).

The equation of a straight line is given by y = mx + b, where m is the slope and b is the y-intercept. However, in the provided equation, the presence of the term -1/x indicates that it is not a straight line, but instead part of the same hyperbolic curve. The straight line aspect would be the x term and the hyperbolic aspect is due to the -1/x term.

User Himanshu Upadhyay
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