# Honors Algebra 2: Piecewise Functions Worksheet 2

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

1. Given $$g(x) = \begin{cases} -x + 12, & \text{if } x < 8 \\ \displaystyle \frac{1}{2}x - 2, & \text{if }x \ge 8 \end{cases}$$
1. Find $$g(-2)$$
2. Solution 14
3. Find $$g(10)$$
4. Solution 3
5. Find $$g(8)$$
6. Solution 2
7. Which is greater, $$g(7.9)$$ or $$g(8.1)$$?
8. Solution $$g(7.9)$$
2. Draw the graph of $$f(x) = \begin{cases} 1, & \text{if } x < 0 \\ 0, & \text{if } x = 0 \\ -1, & \text{if }x > 0 \end{cases}$$
3. Solution
4. Given $$h(x) = \begin{cases} x + 2, & \text{if } x \le 4 \\ 6, & \text{if }x > 5 \end{cases}$$
1. Draw the graph
2. Solution
3. Find $$h(0)$$
4. Solution 2
5. Find $$h(4)$$
6. Solution 6
7. Find $$h(4.5)$$
8. Solution Does Not Exist
9. Find $$h(10)$$
10. Solution 6
5. Given $$f(x) = \begin{cases} 3x + 5, & \text{if } \displaystyle x < \frac{1}{2} \\ 2x + 1, & \text{if } \displaystyle x > \frac{1}{2} \end{cases}$$
1. Find $$f(3)$$
2. Solution 7
3. Find $$\displaystyle f \left( \frac{1}{2} \right)$$
4. Solution Does Not Exist
5. Find $$\displaystyle f \left( \frac{1}{3} \right)$$
6. Solution 6
7. Find $$\displaystyle f \left( \frac{5}{2} \right)$$
8. Solution 6
6. Given $$g(x) = [x]$$ (that is, the greatest integer function)
1. Find $$g(3.2)$$
2. Solution 3
3. Find $$g(1.8)$$
4. Solution 1
5. Find $$g(-2.4)$$
6. Solution -3
7. Find $$g(-6.9)$$
8. Solution -7
7. Given $$h(x) = 3[x + 2] - 1$$ (where $$[x]$$ is the greatest integer function)
1. Find $$h(1.8)$$
2. Solution 8
3. Find $$h(3.1)$$
4. Solution 14
5. Find $$h(-0.4)$$
6. Solution 2
7. Find $$h(-3.1)$$
8. Solution -7
8. Calculators cost $17.95 each if 1 - 10 are purchased,$15.95 each if 11 - 200 are purchased, and $14.50 each if more than 200 are purchased. 1. Write a piecewise function $$C$$ for the cost of $$x$$ calculators. 2. Solution $$C(x) = \begin{cases} 17.95x, & \text{if } x \in \mathbb{Z}; 0 < x \le 10 \\ 15.95x, & \text{if } x \in \mathbb{Z}; 10 < x \le 200 \\ 14.50x, & \text{if } x \in \mathbb{Z}; x > 200 \end{cases}$$ 3. Find $$C(17)$$ 4. Solution$271.15
5. Find $$C(345)$$
6. Solution $5,002.50 9. A gift shop sells pewter mugs for$35. They are currently running an engraving promotion. The first six letters are engraved free. Each additional letter costs 20 cents.
1. Write a piecewise model that gives the price of the mug with $$x$$ engraved letters
2. Solution $$C(x) = \begin{cases} 35, & \text{if } x \in \mathbb{Z}; 0 < x \le 6 \\ 35 + 0.2(x - 6), & \text{if }x \in \mathbb{Z}; 6 < x \end{cases}$$
3. Graph the function
4. Solution
5. What is the price of a mug with the name Jamie Lynn Krane engraved?
6. Solution \$36.60