1. Which interval contains $x = -1$ for the piecewise function $f(x) = \begin{cases} 3x + 7 & \text{if } x \leq -1 \\ x^2 - 2 & \text{if } x > -1 \end{cases}$?
2. What is $f(0)$ for the piecewise function $f(x) = \begin{cases} 2x + 4 & \text{if } x < 1 \\ x^2 - 6 & \text{if } x \geq 1 \end{cases}$?
3. A savings plan applies a rule $f(x)$ to the number of weeks $x$ you have saved. For the piecewise function $$f(x)=\begin{cases}6-x & \text{if } x<4\\ 2x+1 & \text{if } 4\le x<9\\ x^2-10 & \text{if } x\ge 9\end{cases}$$ what is $f(9)$?
4. For the piecewise function $$f(x) = \begin{cases} x + 3 & \text{if } x < -2 \\ -2x & \text{if } -2 \leq x < 3 \\ x^2 - 5 & \text{if } x \geq 3 \end{cases}$$, what is f(3)?
5. What is f(1) for the piecewise function: $$f(x) = \begin{cases} x^2 - 1 & \text{if } x < 1 \\ 3 & \text{if } 1 \leq x < 4 \\ 4x & \text{if } x \geq 4 \end{cases}$$?
6. Which interval contains x = 3 for the function $$f(x) = \begin{cases} 3x + 1 & \text{if } x < 1 \\ 2x - 2 & \text{if } 1 \leq x < 4 \\ x^2 & \text{if } x \geq 4 \end{cases}$$?
7. Based on the piecewise function $$f(x) = \begin{cases} 2x - 3 & \text{if } x < -1 \\ x^2 + 2 & \text{if } -1 \leq x < 2 \\ 5x - 1 & \text{if } x \geq 2 \end{cases}$$, what is f(2)?
8. For the piecewise function $$f(x) = \begin{cases} 3x^2 & \text{if } x < -1 \\ x - 5 & \text{if } -1 \leq x < 2 \\ 2x + 3 & \text{if } x \geq 2 \end{cases}$$, what is f(2)?
9. What is f(2) for the piecewise function: $$f(x) = \begin{cases} -x + 3 & \text{if } x < 1 \\ 4x & \text{if } 1 \leq x < 3 \\ x^2 - 1 & \text{if } x \geq 3 \end{cases}$$?
10. A company assigns a performance rating $f(x)$ based on an employee’s score $x$. The rating function is
$$f(x)=\begin{cases}
7-x & \text{if } x<0 \\
3x+1 & \text{if } 0\le x<4 \\
15 & \text{if } x\ge 4
\end{cases}$$
Based on the piecewise function, what is the value when $x=0$?
11. For the function
$$f(x)=\begin{cases}
2x^2, & x<1\\
6-x, & 1\le x<4\\ \dfrac{x+2}{2}, & x\ge 4
\end{cases}$$
what is $f(4)$?
12. A game assigns points $f(x)$ based on a player’s level $x$ using the piecewise function below. For
$$f(x)=\begin{cases}
3x+2 & \text{if } x<2\\
10 & \text{if } 2\le x<5\\
-x+20 & \text{if } x\ge 5
\end{cases}$$
what is $f(2)$?
13. What is $f(0)$ for the piecewise function $f(x) = \begin{cases} -3x + 4 & \text{if } x < 0 \\ x^2 & \text{if } x \geq 0 \end{cases}$?
14. A machine’s output $f(x)$ depends on the setting $x$ using the piecewise function below. For
$$f(x)=\begin{cases}
-x+6 & \text{if } x<1\\
2x & \text{if } 1\le x<6\\
x^2-10 & \text{if } x\ge 6
\end{cases}$$
what is $f(0)$?
15. A grading policy assigns a score adjustment $f(x)$ based on the raw score $x$. For the piecewise function
$$f(x)=\begin{cases}
-x & \text{if } x<-1\\
2x+5 & \text{if } -1\le x<3\\
11 & \text{if } x\ge 3
\end{cases}$$
what is $f(-1)$?
16. For the function $f(x) = \begin{cases} 3x - 7 & \text{if } x \leq 1 \\ x^2 - 3 & \text{if } x > 1 \end{cases}$, what is $f(1)$?
17. What is $f(-2)$ for the piecewise function $f(x) = \begin{cases} 2x + 3 & \text{if } x < 0 \\ -x^2 + 2 & \text{if } x \geq 0 \end{cases}$?
18. Which interval contains $x = -2$ for the piecewise function $f(x) = \begin{cases} x^2 & \text{if } x \leq -2 \\ 3x + 5 & \text{if } x > -2 \end{cases}$?
19. For the function $f(x) = \begin{cases} 2x - 5 & \text{if } x < -2 \\ x^2 + 3 & \text{if } x \geq -2 \end{cases}$, what is $f(-3)$?
20. For the piecewise function $f(x) = \begin{cases} x^2 + 3 & \text{if } x \leq 0 \\ 2x - 4 & \text{if } x > 0 \end{cases}$, what is $f(1)$?
21. What is f(-3) for the piecewise function: $$f(x) = \begin{cases} 2x^2 & \text{if } x < 0 \\ x + 4 & \text{if } 0 \leq x < 3 \\ 3x - 2 & \text{if } x \geq 3 \end{cases}$$?
22. For the function $$f(x) = \begin{cases} 2 - x & \text{if } x < 0 \\ 3x + 1 & \text{if } 0 \leq x < 3 \\ x^2 & \text{if } x \geq 3 \end{cases}$$, what is f(3)?
23. For the piecewise function
$$f(x)=\begin{cases}
3x+2, & x<2\\
8-x, & 2\le x<6\\
(x-6)^2, & x\ge 6
\end{cases}$$
what is $f(5)$?
24. What is $f(-3)$ for the function defined as $f(x) = \begin{cases} 5x + 1 & \text{if } x < -2 \\ 3x^2 - x & \text{if } x \geq -2 \end{cases}$?
25. A game assigns points based on your score $x$ using the piecewise function shown. For the function $$f(x)=\begin{cases}x-7 & \text{if } x<0\\ 3x+2 & \text{if } 0\le x<4\\ x^2 & \text{if } x\ge 4\end{cases}$$ what is $f(4)$?
26. A taxi company models a surcharge $f(x)$ based on time $x$ (in minutes) with the piecewise function below. For
$$f(x)=\begin{cases}
4 & \text{if } x<2\\
3x+1 & \text{if } 2\le x<8\\
25-x & \text{if } x\ge 8
\end{cases}$$
what is $f(8)$?
27. For the function $$f(x) = \begin{cases} 4x + 1 & \text{if } x < 0 \\ x - 3 & \text{if } 0 \leq x < 5 \\ 2x^2 & \text{if } x \geq 5 \end{cases}$$, what is f(7)?
28. Which interval contains x = 0 for the function $$f(x) = \begin{cases} 5x + 2 & \text{if } x < -2 \\ x^2 & \text{if } -2 \leq x < 1 \\ 3x - 4 & \text{if } x \geq 1 \end{cases}$$?
29. For the piecewise function $$f(x) = \begin{cases} 3x + 2 & \text{if } x < -1 \\ x^2 - 1 & \text{if } -1 \leq x < 2 \\ 4x - 3 & \text{if } x \geq 2 \end{cases}$$, what is f(1)?
30. For the function $$f(x) = \begin{cases} x - 2 & \text{if } x < 1 \\ 5x & \text{if } 1 \leq x < 4 \\ x^2 + 1 & \text{if } x \geq 4 \end{cases}$$, what is f(4)?
31. What is f(-4) for the piecewise function: $$f(x) = \begin{cases} 2x + 3 & \text{if } x < -3 \\ x^2 - 1 & \text{if } -3 \leq x < 1 \\ 4x & \text{if } x \geq 1 \end{cases}$$?
32. For the piecewise function
$$f(x)=\begin{cases}
(x+2)^2, & x<-2\\
5, & -2\le x<1\\
2x-1, & x\ge 1
\end{cases}$$
what is $f(-2)$?
33. Based on the piecewise function
$$f(x)=\begin{cases}
(x+1)^2-1, & x<-1\\
2x+5, & -1\le x<2\\
9-x, & x\ge 2
\end{cases}$$
what is the value when $x=-1$?
34. For the piecewise function
$$f(x)=\begin{cases}
1-x, & x<2\\ \dfrac{x}{2}+3, & 2\le x<6\\
(x-6)+1, & x\ge 6
\end{cases}$$
what is $f(4)$?
35. Based on the piecewise function
$$f(x)=\begin{cases}
4x-1, & x<5\\
(x-5)^2, & 5\le x<8\\
20-x, & x\ge 8
\end{cases}$$
what is the value when $x=6$?
36. Based on the piecewise function
$$f(x)=\begin{cases}
-x+4, & x<0\\
3x+1, & 0\le x<2\\
x^2-1, & x\ge 2
\end{cases}$$
what is the value when $x=2$?
37. What is $f(2)$ for the piecewise function defined below?
$$f(x)=\begin{cases}
9-2x, & x<2\\
3x+1, & 2\le x<6\\ \dfrac{12}{x}, & x\ge 6
\end{cases}$$
38. What is $f(0)$ for the piecewise function defined below?
$$f(x)=\begin{cases}
4x, & x<0\\
(x-2)^2, & 0\le x<5\\
2x-3, & x\ge 5
\end{cases}$$
39. What is $f(-3)$ for the piecewise function defined below?
$$f(x)=\begin{cases}
(x-2)^2, & x<-2\\
4-x, & -2\le x<5\\
2x+1, & x\ge 5
\end{cases}$$
40. A shipping company defines a handling cost $f(x)$ based on package weight $x$ (in pounds). For the piecewise function
$$f(x)=\begin{cases}
9-2x & \text{if } x<1\\
x+4 & \text{if } 1\le x<6\\
2x-1 & \text{if } x\ge 6
\end{cases}$$
what is $f(1)$?
41. A store defines a discount value $f(x)$ based on the number of items $x$ purchased. For the piecewise function
$$f(x)=\begin{cases}
5-x & \text{if } x<0\\
2x+3 & \text{if } 0\le x<5\\
20-x & \text{if } x\ge 5
\end{cases}$$
what is $f(5)$?
42. Which interval contains $x = 1$ for the piecewise function $f(x) = \begin{cases} 2x + 3 & \text{if } x \leq 1 \\ x^2 + 1 & \text{if } x > 1 \end{cases}$?
43. What is $f(0)$ for the piecewise function defined as $f(x) = \begin{cases} 3x + 2 & \text{if } x > 1 \\ x^2 - 4 & \text{if } x \leq 1 \end{cases}$?
44. For the function $f(x) = \begin{cases} x + 2 & \text{if } x \leq -3 \\ 3x - 7 & \text{if } x > -3 \end{cases}$, what is $f(-3)$?
45. For the function
$$f(x)=\begin{cases}
5-x, & x<1\\
2x, & 1\le x<4\\
3x-7, & x\ge 4
\end{cases}$$
what is $f(1)$?
46. What is $f(8)$ for the piecewise function defined below?
$$f(x)=\begin{cases}
3-x, & x<2\\
(x-2)^2, & 2\le x<6\\
2x-5, & x\ge 6
\end{cases}$$
47. For the function $f(x) = \begin{cases} 4x - 3 & \text{if } x < 0 \\ x^2 + 2 & \text{if } x \geq 0 \end{cases}$, what is $f(-1)$?
48. Which interval contains $x = 5$ in the function $f(x) = \begin{cases} 4x - 3 & \text{if } x < 4 \\ x^2 - 1 & \text{if } x \geq 4 \end{cases}$?
49. What is $f(0)$ for the piecewise function $f(x) = \begin{cases} 2x - 5 & \text{if } x < -1 \\ x^2 + 1 & \text{if } x \geq -1 \end{cases}$?
50. A machine outputs a value $f(x)$ based on an input $x$ using the piecewise function. For the function $$f(x)=\begin{cases}x^2+1 & \text{if } x<-1\\ 4-x & \text{if } -1\le x<3\\ 2x & \text{if } x\ge 3\end{cases}$$ what is $f(-1)$?
51. A thermostat uses a rule $f(x)$ to convert an input setting $x$ to an output level. For the piecewise function $$f(x)=\begin{cases}5-x & \text{if } x<2\\ 2x-1 & \text{if } 2\le x<8\\ x+3 & \text{if } x\ge 8\end{cases}$$ what is $f(2)$?
52. For the function $f(x) = \begin{cases} 2x + 5 & \text{if } x < 1 \\ x^2 & \text{if } x \geq 1 \end{cases}$, what is $f(0)$?
53. For the function $f(x) = \begin{cases} -x^2 + 4 & \text{if } x < 2 \\ 2x - 3 & \text{if } x \geq 2 \end{cases}$, what is $f(2)$?
54. Which interval contains $x = 0$ in the piecewise function $f(x) = \begin{cases} 3x - 5 & \text{if } x < 0 \\ x^2 + 1 & \text{if } x \geq 0 \end{cases}$?
55. A shipping company uses a piecewise pricing rule for a package based on its weight $x$ (in pounds). The cost function is
$$f(x)=\begin{cases}
2x+5 & \text{if } x<3 \\
11 & \text{if } 3\le x<7 \\
3x-4 & \text{if } x\ge 7
\end{cases}$$
What is $f(3)$ for the piecewise function defined below?
56. A school uses a piecewise function $f(x)$ to assign points based on the number of late days $x$ for an assignment. The policy is
$$f(x)=\begin{cases}
10-2x & \text{if } x<2 \\
6 & \text{if } 2\le x<5 \\
- x+9 & \text{if } x\ge 5
\end{cases}$$
What is $f(5)$ for the piecewise function defined below?
57. A gym records a membership score using a piecewise function based on the number of visits $x$ in a month. The function is
$$f(x)=\begin{cases}
-x+12 & \text{if } x<4 \\
2x-1 & \text{if } 4\le x<9 \\
20 & \text{if } x\ge 9
\end{cases}$$
Based on the piecewise function, what is the value when $x=8$?
58. A temperature controller outputs a signal $f(x)$ depending on the input reading $x$. The controller follows
$$f(x)=\begin{cases}
5-x & \text{if } x<-2 \\
x^2 & \text{if } -2\le x<3 \\
2x+1 & \text{if } x\ge 3
\end{cases}$$
For the function $f(x)$ above, what is $f(-2)$?
59. A video game assigns a bonus $f(x)$ based on the player’s level $x$. The bonus rule is
$$f(x)=\begin{cases}
2x & \text{if } x<5 \\
10-x & \text{if } 5\le x<10 \\
1 & \text{if } x\ge 10
\end{cases}$$
Based on the piecewise function, what is the value when $x=10$?
60. A lab uses a piecewise calibration function $f(x)$ for a sensor reading $x$. The calibration is
$$f(x)=\begin{cases}
3x+2 & \text{if } x\le -1 \\
-x^2+4 & \text{if } -1<x<2 \\
2x-3 & \text{if } x\ge 2
\end{cases}$$
For the function $f(x)$ above, what is $f(-1)$?
61. A taxi company models a fare adjustment $f(x)$ based on the distance $x$ (in miles). The adjustment is
$$f(x)=\begin{cases}
4 & \text{if } x<2 \\
2x+1 & \text{if } 2\le x<6 \\
x^2-10 & \text{if } x\ge 6
\end{cases}$$
What is $f(6)$ for the piecewise function defined below?
62. A taxi fare adjustment is modeled by a piecewise function of time $x$ (in minutes). For the function $$f(x)=\begin{cases}8 & \text{if } x<5\\ x+3 & \text{if } 5\le x<12\\ 20-2x & \text{if } x\ge 12\end{cases}$$ what is $f(12)$?
63. A store’s coupon value depends on the purchase amount $x$ (in dollars) using the piecewise function below. For the function $$f(x)=\begin{cases}0.5x & \text{if } x<10\\ x-3 & \text{if } 10\le x<20\\ 2x-25 & \text{if } x\ge 20\end{cases}$$ what is $f(10)$?
64. A teacher uses a curve $f(x)$ to adjust a raw score $x$. For the piecewise function $$f(x)=\begin{cases}x+10 & \text{if } x<50\\ 2x-40 & \text{if } 50\le x<70\\ x-5 & \text{if } x\ge 70\end{cases}$$ what is $f(69)$?
65. A sensor converts a reading $x$ into an alert level $f(x)$ using the piecewise function below. For the function $$f(x)=\begin{cases}3x & \text{if } x<1\\ x^2+2 & \text{if } 1\le x<4\\ 14-x & \text{if } x\ge 4\end{cases}$$ what is $f(0)$?
66. A video platform sets a recommendation score $f(x)$ based on watch time $x$ (in hours) using the piecewise function. For the function $$f(x)=\begin{cases}x+4 & \text{if } x<2\\ 9-2x & \text{if } 2\le x<5\\ x^2-1 & \text{if } x\ge 5\end{cases}$$ what is $f(3)$?
67. For the function $$f(x) = \begin{cases} x^2 + 1 & \text{if } x < 0 \\ 3x - 4 & \text{if } 0 \leq x < 3 \\ 2x + 5 & \text{if } x \geq 3 \end{cases}$$, what is f(-1)?
68. Based on the piecewise function $$f(x) = \begin{cases} -3x + 1 & \text{if } x < 0 \\ x^2 + 3x & \text{if } 0 \leq x < 2 \\ 2x - 7 & \text{if } x \geq 2 \end{cases}$$, what is f(0)?
69. For the function $$f(x) = \begin{cases} -x^2 + 4 & \text{if } x < 1 \\ 2x & \text{if } 1 \leq x < 4 \\ 3x - 1 & \text{if } x \geq 4 \end{cases}$$, what is f(3)?
70. For the function
$$f(x)=\begin{cases}
\dfrac{x}{3}, & x<0\\
2x-4, & 0\le x<3\\
(x-3)^2-2, & x\ge 3
\end{cases}$$
what is $f(3)$?
71. Which interval contains $x = 3$ in the piecewise function $f(x) = \begin{cases} x - 2 & \text{if } x < 3 \\ 2x + 5 & \text{if } x \geq 3 \end{cases}$?
72. For the function $f(x) = \begin{cases} x^2 + 2x & \text{if } x < 1 \\ 2x - 5 & \text{if } x \geq 1 \end{cases}$, what is $f(1)$?
73. For the function $f(x) = \begin{cases} -2x + 6 & \text{if } x < 3 \\ x^2 - 2 & \text{if } x \geq 3 \end{cases}$, what is $f(4)$?
74. For the function $$f(x)=\begin{cases} -x^2, & x<-3 \\ 2x+1, & -3\le x<0 \\ (x+1)^2, & x\ge 0 \end{cases}$$ what is $f(-3)$?
75. Based on the piecewise function
$$f(x)=\begin{cases}
2-x, & x<-4\\
(x+4)(x-1), & -4\le x<1\\
3, & x\ge 1
\end{cases}$$
what is the value when $x=-4$?