Question

How do you find the domain and range of a piecewise linear function?

Answer 1

To find the domain and range of a piecewise linear function, examine each piece for x and y value limitations, then combine results for the complete domain and range. X, Y, and Z are random variables with specific domains, and a negative value for Z is not possible. A discrete probability distribution must have non-negative probabilities that sum to one.

Step-by-step explanation:

To find the domain and range of a piecewise linear function, you will follow several steps:

• Examine each piece of the function and note the restrictions on the x-values (domain).
• For each piece of the function, determine the y-values produced (range).
• Combine the results from each piece, ensuring that overlaps in domain are addressed by including all x-values that give y-values in the function.
• Similarly, combine the y-values (range) from each piece to include all possible y-values the function can produce.

Consider the domains provided in the reference information:

1. The domain of X, representing a student's major, is finite and categorical, listing all possible majors offered.
2. The domain of Y, the number of classes taken in the previous semester, is a set of non-negative integers reflecting the possible number of classes.
3. The domain of Z, the amount of money spent on books in the previous semester, starts from zero and can be any positive number.

X, Y, and Z are considered random variables because they can take on any value within their domains, and their specific values are not known until a survey or study is completed. Money spent on books (Z) having a value of -7 would not be a possible value, as the domain starts from zero and does not include negative numbers.

In terms of probability distribution for a discrete random variable, the two essential characteristics are:

• The probabilities are non-negative.
• The sum of the probabilities is one.

Answer 2

A piecewise linear function is a function that will have two equations with an inequality beside it dependent on the variable. For instance, If x is less than something, you use one equation, and if x is greater than something, you use the second equation. If given an integer, then the highest and lowest points will become you domain and range. The lowest and highest points of x will be your domain, while the same is true for range with the exception of operating under y values. Hope this helped.