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The family of curves represented by the equation y = kx^n, where n is a constant

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Question: The family of curves represented by the equation y = kx^n, where n is a constant, is known as:

Options:

  1. Polynomial curves
  2. Rational curves
  3. Trigonometric curves
  4. Exponential curves

Correct Answer: Polynomial curves

Solution: 

The equation y = kx^n represents a family of polynomial curves.

The family of curves represented by the equation y = kx^n, where n is a constant

Practice Questions

Q1
The family of curves represented by the equation y = kx^n, where n is a constant, is known as:
  1. Polynomial curves
  2. Rational curves
  3. Trigonometric curves
  4. Exponential curves

Questions & Step-by-Step Solutions

The family of curves represented by the equation y = kx^n, where n is a constant, is known as:
  • Step 1: Identify the equation given, which is y = kx^n.
  • Step 2: Recognize that 'k' is a constant that can change the shape of the curve.
  • Step 3: Understand that 'n' is also a constant that determines the degree of the polynomial.
  • Step 4: Realize that as 'k' changes, you get different curves, but they all follow the same basic form.
  • Step 5: Conclude that the equation y = kx^n represents a family of curves known as polynomial curves.
  • Family of Curves – The equation y = kx^n represents a family of curves where k and n define the specific shape and behavior of the polynomial.
  • Polynomial Functions – The equation is a polynomial function, which is characterized by its degree (n) and coefficients (k).
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