Final answer:
The range of values for x can refer to an interval of real numbers within which x may fall; for example, between 1.5 and 4.5, inclusive. It can also result from statistical calculations, such as x values within a certain number of standard deviations from the mean, or relate to the domain over which a function is defined.
Step-by-step explanation:
When you are asked to identify the range of values for x, you are determining the set of possible x-values specified by the given conditions or within a particular context. For example, the statement '1.5 ≤ x ≤ 4.5' tells us that x can be any number between 1.5 and 4.5, inclusive. This defines a continuous range where each point is as probable as any other within this interval.
In statistics, the range of a normal distribution within certain standard deviations from the mean can also specify the range of x. For instance, if we know that 95% of x values lie within two standard deviations (represented by '2σ') of the mean, we can calculate this range using the given standard deviation and mean values. The statement 'About 95 percent of the x values lie between -20 = (-2)(6) = −12 and 2σ = (2)(6) = 12' is an application of this principle.
In probability, to calculate the chance that x falls between two values, we might be asked to shade the region between x = 2.3 and x = 12.7 on a graph, which visually represents the probability of x falling within that range.
Lastly, the range of x values can also be set by functions within specific domains, such as 'For the function f(x), 0 ≤ x ≤ 20' indicating x is a real number anywhere from 0 to 20, inclusive.