Exploring Power Functions: The Graphical Shape And Applications In Science And Engineering

power function

y=Cx^k

A power function is a mathematical function of the form f(x) = kx^n, where k and n are constants and x is the variable. The power function is named so because the variable is raised to a power (n) in the function.

The value of n determines the shape of the graph of the function. When n is positive and even (e.g., n=2,4,6), the graph is a concave-upward (or U-shaped) curve. When n is odd (e.g., n=1,3,5), the graph is a concave-downward (or inverted U-shaped) curve.

The constant k affects the vertical position of the graph. When k is positive, the graph is shifted upward, and when k is negative, the graph is shifted downward. If k=1, the graph passes through the origin (0,0).

Power functions have many applications in science and engineering, for example, in the modeling of population growth, radioactive decay, and electrical resistance.

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