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Identify the domain and range of the rational function given:

Identify the domain and range of the rational function given:-example-1
User Mikemil
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1 Answer

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Answer:

  • domain: all real numbers except -1 and +1; (-∞, -1) ∪ (-1, 1) ∪ (1, ∞)
  • range: all real numbers; (-∞, ∞)

Explanation:

You want the domain and range of the function shown in the graph, which has vertical asymptotes at x = ±1, a zero at x = 0, and a horizontal asymptote of y = 0.

Domain

The domain is the set of x-values for which the function is defined. The given function has vertical asymptotes at x = ±1, so it is undefined for those values of x.

The domain is all real numbers except x = ±1.

Range

The range is the set of numbers the function can have as output values. Ordinarily, a function does not actually have a value equal to its horizontal asymptote. In this case, the function crosses the x-axis at x=0, so does have y=0 as an output value there. Hence any real number may be an output value of this function.

The range is all real numbers.

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User Vicent Marti
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