The diagonal of a unit square, for example, is radical(2).
a function whose range is in the real number
y = cuberoot(x) for real x is not a rational function.
No. You can always "cheat" to prove this by simply giving the function's domain a bound.Ex: f: [0,1] --> RI simply defined the function to have a bounded domain from 0 to 1 mapping to the codomain of the set of real numbers. The function itself can be almost anything, periodic or not.Another way to "cheat" is to simply recognize that all functions having a domain of R are bounded functions, by definition, in the complex plane, C.(Technically, you would say a non-compact Hermitian symmetric space has a bounded domain in a complex vector space.) Obviously, those functions include non-periodic functions as well.
Rational function can be used in real life in modeling multi-person work problems.
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The domain of the sine function is [-infinity, +infinity].The range is [-1, +1].The sine function is periodic. It repeats itself every 360 degrees or 2PI radians.
A nonconstant function is called periodic if there exists a number that you can add to (or subtract from) the argument and get the same result. The smallest such positive number is called the period. That is, nonconstant function f(x) is periodic, if and only if f(x) = f(x + h) for some real h. The smallest positive such h is the period. For example, the sine function has period 2*pi, and the function g(x) := [x] - x has period 1.
Since cosh is based on the exponential function, it has the same period as the exponential function, namely, 2 pi i.Note: If you consider only the real numbers, the exponential function, as well as cosh, are NOT periodic.
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A real world example of a cubic function might be the change in volume of a cube or sphere, depending on the change in the dimensions of a side or radius, respectively.
The diagonal of a unit square, for example, is radical(2).
a function whose range is in the real number
A real-world example of periodic motion is the swinging of a pendulum, such as in a grandfather clock. The pendulum swings back and forth in a regular and repeating motion, controlled by the force of gravity.
Explain the purpose of a periodic performance report (two benefits)
Domain of the logarithm function is the positive real numbers. Domain of exponential function is the real numbers.
For someone packing whole house the cubic function is important to factor the amount of storage needed to move a home. Another real application would be in manufacturing and filling a box with product.