The family of curves y = kx^n, where n is a constant, represents:

₹0.0

Question: The family of curves y = kx^n, where n is a constant, represents:

Options:

Correct Answer: Polynomial functions

Solution:

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

The family of curves y = kx^n, where n is a constant, represents:

The family of curves y = kx^n, where n is a constant, represents:

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 since the equation is in the form of k times x raised to a power (n), it represents polynomial functions.

Family of Curves – The equation y = kx^n represents a family of curves where k and n define the specific shape and position of the polynomial functions.
Polynomial Functions – The expression y = kx^n is a polynomial function of degree n, which varies based on the value of n.