Let's go through the questions from the image and provide solutions.

1. A function is ______ a relation, but not all relations are functions.

   • Answer: c. always

2. What is the domain of this function: {(1, 1), (3, 5), (4, 6), (8, 9)}?

   • Answer: a. {1, 3, 4, 8}

3. What is the range of this function: {(1, 0), (2, 0), (−1, 5)}?

   • Answer: b. {0, 5}

4. Which of the following relations is a function?

   • Answer: b. {(3, 7), (3, 6), (5, 3)}

5. Given f(x) = x − 1, find f(1).

   • Answer: a. 0

6. If g(x) = 2x² − 7, what is f(−2)?

   • Answer: b. 1

7. Which of the following is the domain of y = 2x + 1?

   • Answer: a. {x/x ∈ R}

8. What is the symbol for the inverse of a function?

   • Answer: a. f⁻¹(x)

9. It is a function defined by two or more formulas on different parts of its domain.

   • Answer: b. Piecewise

10. Which of the following is a piecewise function?

• Answer: d. f(x) = {−18x + 20, x < 19; −16x², x ≥ 19}

11. Evaluate the function f(x) = x² − 3, at x = 3.

• Answer: d. 9

12. If f(x) = x² − x and g(x) = x + 2, what is f(g(x))?

• Answer: c. x² + 4

13. Perform the indicated operation: f(x) = x² − x − 2, g(x) = x + 1. Find f + g(x).

• Answer: c. x² − 3x − 2

14. Use item #13 in finding (f ∘ g)(1).

• Answer: b. 1

15. Given f(x) = x² − 4x + 4, Solve for f(0).

• Answer: d. 4

16. If f(x) = (x − 3)/(x + 4) and g(x) = (x + 1)/(x + 4), find (f − g)(x).

• Answer: c. (x − 4)/(x + 4)

17. Given f(x) = x − 5 and g(x) = x² − 1, Find (f ∘ g)(x).

• Answer: c. x² − 5x − 6

18-19. Answer missing (left for student to solve).

20-21. Answer missing (left for student to solve).

22. Find (g ∘ f)(x) from item number 20.

• Answer: (likely involves composition, answer cannot be confirmed without item 20 info)

23. What is the degree of the polynomial function p(x) = 14 + 4x − 3x³?

• Answer: d. 3

24. Which of the following is a rational function?

• Answer: b. g(x) = 7x³ − 4√x + 1 / x² + 3

25. Which of the following functions is not rational?

• Answer: d. f(x) = (x² − 9) / (x − 3)

26. Which family of functions does y = e^x − 4 belong to?

• Answer: b. Exponential

Would you like details for any specific questions or further clarifications?

Here are 5 related questions to explore further:

1. What is the difference between a relation and a function?
2. How do you determine the range of a function given its domain?
3. What conditions must a relation satisfy to be classified as a function?
4. How do you find the inverse of a function step by step?
5. What are some real-world applications of piecewise functions?

Tip: To verify if a relation is a function, check if each input (x-value) has exactly one output (y-value).