# Honors Algebra 2: Piecewise Functions Worksheet 1

• Class: Honors Algebra 2
• Author: Peter Atlas
• Text: Algebra and Trigonometry: Structure and Method, Brown

Given

 $$f(x) = \begin{cases} 3x - 7, & \text{if } x \leq 2 \\ 6 - 2x, & \text{if }x > 2 \end{cases}$$ $$g(x) = \begin{cases} 3x + 5, & \text{if } x < 5 \\ -x + 3, & \text{if } x \geq 5 \end{cases}$$ $$h(x) = \begin{cases} \displaystyle \frac{2}{3}x + 1, & \text{if } x < -3 \\ 2x - 3, & \text{if } x \geq -3 \end{cases}$$
1. Find $$f(0)$$.
2. Solution -7
3. Find $$f(2)$$.
4. Solution -1
5. Find $$f(4)$$.
6. Solution -2
7. Find $$f(-3)$$.
8. Solution -16
9. Find $$g(5)$$.
10. Solution -2
11. Find $$g(-4)$$.
12. Solution -7
13. Find $$g(3)$$.
14. Solution 14
15. Find $$g(10)$$.
16. Solution -7
17. Find $$h(-9)$$.
18. Solution -5
19. Find $$h(-3)$$.
20. Solution -9
21. Find $$h(6)$$.
22. Solution 9
23. Find $$h(1)$$.
24. Solution -1
25. Graph $$f(x) = \begin{cases} 3, & \text{if } x \leq 4 \\ -1, & \text{if } x > 4 \end{cases}$$
26. Solution
27. Graph $$f(x) = \begin{cases} x - 4, & \text{if } x < 2 \\ 3 - x, & \text{if } x \geq 2 \end{cases}$$
28. Solution
29. Graph $$f(x) = \begin{cases} x + 1, & \text{if } x < 0 \\ -x + 1, & \text{if } 0 \leq x \leq 2 \\ x - 2, & \text{if } x > 2 \end{cases}$$
30. Solution
31. Graph $$f(x) = \begin{cases} 2x, & \text{if } x \geq -1 \\ 3x, & \text{if } -2 < x < -1 \\ -x, & \text{if } x \leq -2 \end{cases}$$
32. Solution
33. Graph $$f(x) = \begin{cases} 2, & \text{if } x \leq -3 \\ -1, & \text{if } -3 < x < 3 \\ 3, & \text{if }x \geq 3 \end{cases}$$
34. Solution
35. Write the piecewise function whose graph would look like the graph below.
36. Solution $$f(x) = \begin{cases} (x - 1) - 2, & \text{if } x > 1 \\ -2x + 2, & \text{if }x \le 1 \end{cases}$$
37. Write the piecewise function whose graph would look like the graph below.
38. Solution $$f(x) = \begin{cases} (x - 1) - 2, & \text{if } x \ge 1 \\ -2x + 2, & \text{if } x < 1 \end{cases}$$
39. Write the piecewise function whose graph would look like the graph below.
40. Solution $$f(x) = \begin{cases} (x - 1) - 2, & \text{if } x > 1 \\ -1, & \text{if } x = 1 \\ -2x + 2, & \text{if }x < 1 \end{cases}$$
41. A company provides bus tours of historical cities. The given function describes the rate for small groups and the discounted rate for larger groups, where $$x$$ is the number of people in your group:
$$C(x) = \begin{cases} 8.95x, & \text{if } x \in \mathbb{Z} ; 0 < x \leq 10 \\ 7.50x, & \text{if } x \in \mathbb{Z} ; x > 10 \end{cases}$$
1. Graph the function.
2. Solution
3. Identify the domain of the function
4. Solution $$\{ x \mid x \in \mathbb{Z}; x > 0 \}$$
42. You are employed by a company in which commission rates are based on how much you sell. If you sell up to $100,000 of merchandise in a month, you earn 5% of sales as a commission. If you sell over$100,000, you earn 8% commission on your sales. Write a piecewise function that gives the amount you earn in commission in a given month for $$x$$ dollars in sales.
43. Solution $$C(x) = \begin{cases} 0.05x, & \text{if } 0 < x \le 100,000 \\ 0.08x, & \text{if }x > 100,000 \end{cases}$$