Explain how to find the range of possible values.

To find the range of possible values, identify the minimum and maximum values within a given set or function.

To start, you need to understand what the range of possible values means. In mathematics, the range is the difference between the highest and lowest values in a set of numbers or the output values of a function. For a set of numbers, you simply look for the smallest and largest numbers. For example, if you have the set {3, 7, 2, 9, 5}, the minimum value is 2 and the maximum value is 9. Therefore, the range of this set is from 2 to 9.

When dealing with functions, the process involves a bit more analysis. If you have a function, say \( f(x) = 2x + 3 \), you need to determine the values that \( f(x) \) can take. This often involves looking at the domain (the set of all possible input values) and then seeing what output values these inputs produce. For linear functions like \( f(x) = 2x + 3 \), the range is all real numbers because as \( x \) takes any real number, \( f(x) \) will also cover all real numbers.

For more complex functions, such as quadratic functions \( f(x) = x^2 - 4 \), you need to find the vertex of the parabola to determine the minimum or maximum value. Here, the vertex is at \( (0, -4) \), so the minimum value of \( f(x) \) is -4, and since the parabola opens upwards, the range is all values \( y \geq -4 \).

In summary, finding the range involves identifying the smallest and largest values in a set or analysing the output values of a function based on its domain.