Intermediate Algebra worksheet focusing on relations and functions, including domain and range exercises.

Looking at the image, I can see it’s a worksheet titled “Intermediate Algebra, 3/e” by Margaret L. Lial, Chapter 25: Relations and Functions, Section 25-4, Practice Test.

There are 8 problems listed. Since the user didn’t specify which problem to solve, and given that this is a practice test with multiple questions, I’ll assume they want me to solve the first problem as an example — unless otherwise specified.

Problem 1 says:
> Find the range of the relation {(3, 1), (1, -2), (0, 4), (2, 1).
> a) {3, 1, 0, 2}
> b) {1, -2, 4}
> c) {0, 1, 2, 3}
> d) {0, 1, 4}

Let me solve this step by step.

Step 1: Understand what “range” means.
In a relation (which is just a set of ordered pairs), the range is the set of all second numbers (the y-values). The domain is the set of all first numbers (the x-values).

Step 2: List the ordered pairs:
(3, 1), (1, -2), (0, 4), (2, 1)

Step 3: Extract the second numbers (y-values):
From (3, 1) → 1
From (1, -2) → -2
From (0, 4) → 4
From (2, 1) → 1

So the y-values are: 1, -2, 4, 1

Step 4: Remove duplicates (since sets don’t repeat elements).
Unique values: {-2, 1, 4}

Step 5: Match with answer choices.
a) {3, 1, 0, 2} → these are x-values (domain), not range → wrong
b) {1, -2, 4} → matches our result → correct
c) {0, 1, 2, 3} → again, domain values → wrong
d) {0, 1, 4} → missing -2, has 0 which isn’t in range → wrong

Final Answer: b) {1, -2, 4}