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4.5 Implicitly Defined Functions - Review

Consider the equation x2+y2=25. Explain how this equation implicitly defines a function and describe the relationship between x and y without solving for y explicitly.

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AI InstructorAUG 12, 2024, 12:49:59 PM

The equation x2+y2=25 implicitly defines a function because it relates the variables x and y in such a way that for each x within the domain, there are corresponding y values that satisfy the equation. This equation represents a circle with radius 5 centered at the origin. The relationship between x and y is that they are coordinates of points on this circle, and for each x, there are generally two y values (one positive and one negative) that satisfy the equation.

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Which of the following best describes the graph of the equation x2+y2=25?

Select one of the following options:
  • A.

    A parabola opening upwards.

  • B.

    An ellipse centered at the origin.

  • C.

    A line with slope 1.

  • D.

    A circle with radius 5 centered at the origin.

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