Chapter 4 - Functions
Page 3 of 15
|Functions - Function Domain - Contents|
The function domain is the set of elements that contain the independent variable x in any function y = f(x). It is all possible numbers that can be used for the x variable. The domain is established by the nature of the function itself. The domain of a function can also be constricted by definition. The domain for a mathematic equation must unambiguously describe a set of elements that is either finite or infinite. If the domain is not expressly defined or restricted within a mathematic function then it is presumed to be the entire set of real numbers. An example of a domain inherently restricted by the nature of the equation is f(x) = square root of x. Here the square root of a negative number does not exist, so the equation itself limits the domain of x to zero and the positive numbers. The domain of a function can be finite or infinite.
|Functions - Function Domain - Examples|
If the function is y = f(x),
a definition for the domain could be one of the following,
for all x where x is an integer between 0 and 10,
for all x where x > 2,
for all x where x = 12.
If y = f(x) is y = x + 1,
y equals x plus one,
then the domain of x is the set of real numbers.
If y = f(x) is y = square root of x,
then the domain is x >= 0.
|Functions - Sections - Chapters|
|1 - Function Definition||2 - Function Notation||3 - Function Domain|
|4 - Function Range||5 - Composite Functions||6 - Inverse Functions|
|7 - Linear Functions||8 - Power Functions||9 - Quadratic Functions|
|10 - Logarithmic Functions||11 - Exponential Functions||12 - Factorial Functions|
|13 - Limit Functions||14 - Summation Functions||15 - Percentage Functions|
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