Cue the memories from the Advanced Math classes we took in high school. The endless hours were spent trying to understand the relative functions. And what exactly is the distinction between domain and range. Domain and range are a part of solving problems with functions that fall under physical science. The domain and range of a function play a critical role in the method of approach to solving the said problem.
Domain vs Range
The main difference between domain and range is that while domain refers to the values present in the set that is used in describing a function, range, on the other hand, is used in reference to the values present in the set that contains the values that the function is capable of taking.
The domain of a function is the set representation of the values for which the mathematical function is defined. A domain is referred to as the independent variable in any given function. Put simply; the domain refers to the values of the input that the function is capable of having.
The range of a function is the set representation of the values for which the mathematical function can take presence. The range of any function is considered to be a dependent variable, unlike its counterpart. The range contains the outputs of a given function after it is solved mathematically to obtain the solution.
Comparison Table Between Domain and Range
Parameters of Comparison | Domain | Range |
Definition | It can be referred to as the acceptable set of inputs. | The range of any function is defined as the set of resulting values. |
Dependency | It consists of independent variables. | It consists of dependent variables, unlike its counterpart. |
Axis | The mathematical domain of any function is measured alongside the X-axis. | The range of a function is measured alongside the Y-axis to obtain the values. |
Consists of | It consists of all the probable input values. | All probable output values are recorded in the set. |
Example | The time between sunrise and sunset. | Elevation of the sun at any given point. |
What is Domain?
Domain refers to the intangible set of values that defines a mathematical function. It is a part of relations and functions
It has to be noted that the domain of a function is not a property of the function; rather, it is the definition of the given function.
Domains are independent variables that cannot be influenced by any other element used in the calculation.
It can be described as the input values that a function has. Furthermore, all the functions are limited to the domain’s subsets.
Used in reference to the set of inputs that the function can accept.
Domains are generally measured alongside the X-axis in a graph when computing the values. The X-axis lies horizontally in any given graphical representation.
The value of the domain differs depending on the type of function that is being solved. Every mathematical problem has a varying set of domain values.
The domain values for the cosine function include all real numbers over and below zero. The set also includes the value of zero. However, the domain values for a square root cannot be lesser than zero.
The domain of a function is written as f: x->y, wherein the domain of f is x.
A real-life example would be the time between sunrise and sunset; this period includes all the domain values.
What is Range?
The range of the function includes the values of a mathematical function that can exist. It basically sums up the output values of the function.
The range of a function is a dependent variable. It cannot exist individually. The domain of a function plays a critical part in helping determine the set values of the range.
The solutions of the function that are solved mathematically consist of the range set of the said function.
The range of a function is often associated with the image of the given function and the codomain of the function.
A dependent variable, its value is derived using mathematical applications and solving the function mathematically.
The function’s range is typically represented in the Y-axis. The Y-axis of a graph is located vertically in any given quadrant.
The value of the range cannot be calculated without the knowledge of the set values of the domain. When the domain value of a function y=f(x) is x, y would be considered as its range.
One of the easiest examples of a real-life range is the sun’s altitude in the axis from zero to the maximum elevation on a given latitude and time.
The range is a codependent variable that consists of the outputs of the given or mentioned function.
Main Differences Between Domain and Range
- Domain and range are a part of mathematical relations and functions. The domain holds within it the inputs, whereas the range is a sum of all of the outputs.
- The domain is independent, while the range is dependent on the former to find the values.
- Domain is situated alongside the horizontal x-axis, while the range is located on the y-axis that is represented vertically.
- The domain includes what is included in a function. Meanwhile, the range talks about the function’s result in lieu of the domain values.
- The rising and the sun‘s setting can be considered an example of the domain. The altitude of the sun at a given point of time is its resultant range.
Conclusion
An integral part of mathematical studies, the domain and range are concepts used in physical sciences to solve the functions and relations of any given equation.
The domain consists of the input values of a function and helps in its definition. It is independent and is an essential component in solving the problem.
The range includes all of the values that are listed to be counted as the output of the problem in question. It is dependent on the domain to help find all possible outcomes that an existing function can have.
The advanced math classes we took in our high school tried to teach us about applying domain and range in real-life situations.
References
- https://link.springer.com/content/pdf/10.1007/0-306-47204-X.pdf#page=361
- http://pbc.biaman.pl/Content/24034/1990%20nr%202.pdf#page=73