Final answer:
Writing the domain and range as inequalities involves describing the set of all possible x-values and y-values for which a function is defined, respectively. The domain might be written as -3 ≤ x < 10, while the range could be expressed as 2 ≤ y < 6. In statistics, inequalities are also used in defining the alternative hypothesis.
Step-by-step explanation:
When writing the domain of a function as an inequality, you are describing the set of all possible input values (typically x-values) for which the function is defined. For example, if a function is defined for all x greater than or equal to -3 but less than 10, you can write this domain as -3 ≤ x < 10.
Similarly, the range of a function is the set of all possible output values (typically y-values) after applying the function to its domain. For instance, if a function's output values are always greater than or equal to 2 but less than 6, the range can be expressed as 2 ≤ y < 6.
In the context of hypothesis testing in statistics, the alternative hypothesis (H1 or H₁) uses inequality symbols to suggest a relationship that is different from the null hypothesis. The symbols often used are not equal to (<>, ≠), less than (<), and greater than (>). An example of writing the alternative hypothesis might be H₁: μ < 10, where μ is the population mean.