Algebra – Part 10: Domain and Range

This time, we’ll take a look at domain and range.

Domain and range concept:

In mathematics, the domain and range are concepts that describe the input and output of a function, respectively.

The domain of a function is the set of all possible input values for which the function is defined. In other words, it is the set of all values of the independent variable that can be plugged into the function to produce a valid output. The domain can be expressed in different ways, depending on the type of function. For example, for a polynomial function, the domain is usually all real numbers, while for a rational function, the domain is all real numbers except for the values that make the denominator zero.

The range of a function, on the other hand, is the set of all possible output values that the function can produce, given all possible inputs from its domain. In other words, it is the set of all values of the dependent variable that the function can take on. The range can also be expressed in different ways, depending on the type of function. For example, for a linear function, the range is all real numbers, while for a trigonometric function, the range is usually a specific subset of the real numbers, depending on the function.

In summary, the domain and range are important concepts in mathematics that help to define the input and output of a function, respectively. They are both essential to understanding the behavior and properties of functions in various mathematical contexts.

Example 1:

Here’s the problem.

And here’s a more detailed explanation. f is for function and f(x) represents y, which is the dependent part of the equation, meaning the output of y depends on what kind of answer can be drawn from the independent part of it – 3(x)² + 6x – 2.

And this is the graphical output of the equation.

From here, let’s try more challenges.

Example 2:

Example 3:

Example 4:

Example 5:

Example 6: