Definition of Range

The range of a function is the set of all possible output values (y-values) that the function can produce. In other words, it is the set of all values that the function can “reach” or “hit” when you plug in different input values (x-values).

Example

Let’s say we have the function f(x) = x^2. If we plug in different values of x, we get different values of y:

• f(0) = 0^2 = 0
• f(1) = 1^2 = 1
• f(2) = 2^2 = 4
• f(3) = 3^2 = 9
• …

So the range of this function is the set of all possible y-values, which is {0, 1, 4, 9, …}.

Finding the Range

There are different methods for finding the range of a function, depending on the type of function and the information given. Here are some general steps:

1. Find the domain of the function, which is the set of all possible input values (x-values).
2. Use algebraic or graphical methods to determine the output values (y-values) that correspond to the domain.
3. Write the range as a set of numbers or a description of the pattern.

For example, if we have the function g(x) = 2x – 1, we can:

1. The domain is all real numbers, since we can plug in any value of x.
2. We can use a table or a graph to see that the output values range from negative infinity to positive infinity, since the slope is positive and the y-intercept is negative.
3. So the range is (-∞, ∞), which means all real numbers.

Conclusion

The range of a function is an important concept in mathematics, as it helps us understand the behavior and limitations of functions. By knowing the range, we can determine whether a function is one-to-one, onto, or neither, and we can use it to solve problems in various fields, such as physics, engineering, and economics. So next time you encounter a function, don’t forget to ask yourself: what is the range of this function?