Part 4/5:
presents a specific parabolic structure, while a more complex function such as
[
f(x) = \frac{x^{2/3}}{(x - 2)^2}
]
shows an entirely different curvature and behavior, demonstrating the diversity inherent in algebraic functions.
Real-Life Application: The Theory of Relativity
An interesting real-world application of algebraic functions can be found in the theory of relativity, where mass ( m ) can be expressed as a function of velocity ( v ):
[
m(v) = m_0 \sqrt{1 - \frac{v^2}{c^2}}
]
Here, ( m_0 ) is the rest mass and ( c ) represents the speed of light. This equation illustrates how, as velocity approaches the speed of light, the mass of an object increases, hinting at the profound implications of relativity.