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

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

Options:

Correct Answer: Polynomial curves

Solution:

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

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

The family of curves represented by 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' and 'n' vary, different curves are formed, but they all follow the same general form.
Step 5: Conclude that this equation represents a family of polynomial curves because it is a polynomial function of x.

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 expression y = kx^n is a polynomial function, which is a fundamental concept in algebra and calculus.