Question

Область определения функции y=2/x

Answer 1

Т.к знаменатель не может обращаться в нуль, значит

$D(y)=(-\infty,0)U(0,+\infty)$

Answer 2

Function Definition of y=2/x

The function y=2/x can be defined as follows:

Domain and Range: - The domain of the function y=2/x is all real numbers except x=0. - The range of the function y=2/x is all real numbers except y=0.

Graph: - The graph of the function y=2/x is a hyperbola that approaches the x and y axes but never touches them.

Behavior as x Approaches Positive and Negative Infinity: - As x approaches positive infinity, y approaches 0. - As x approaches negative infinity, y also approaches 0.

Behavior as x Approaches 0 from the Positive and Negative Sides: - As x approaches 0 from the positive side, y approaches positive infinity. - As x approaches 0 from the negative side, y approaches negative infinity.

Additional Information

- The function y=2/x is a rational function, and its graph exhibits asymptotic behavior as x approaches positive and negative infinity. - The function has a vertical asymptote at x=0, which means the graph approaches but never crosses the y-axis.

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