Question 1: Determine the domain and range of the function f(x) = x^2 + 3.

Answer: {"range":"[3, ∞)","domain":"all real numbers"}

Question 2: Identify the domain and range of the function g(x) = √(x - 2).

Answer: {"range":"[0, ∞)","domain":"[2, ∞)"}

Question 3: For the function h(x) = 5 / (x - 4), state the domain and range.

Answer: {"range":"all real numbers except 0","domain":"x ≠ 4"}

Question 4: Plot the graph of y = 2x + 1 on the provided grid. What is the domain and range?

Answer: {"range":"all real numbers","domain":"all real numbers"}

Question 5: Construct a parabola with vertex at (1, 2) and passing through (2, 3). Determine its domain and range.

Answer: {"range":"[2, ∞)","domain":"all real numbers"}

Question 6: A real-world scenario: The temperature T(x) in Celsius over hours x = 0 to 24 hours is modeled by T(x) = -0.05x^2 + 1.2x + 15. What is the domain and range of this temperature function?

Answer: {"range":"[15, maximum temperature]","domain":"[0, 24]"}

Question 7: Given h(x) = 3x / (x + 2), identify the domain and range. Explain any restrictions.

Answer: {"range":"all real numbers except 0","domain":"x ≠ -2"}

Question 8: Analyze the function f(x) = ln(x - 5). What are its domain and range? Identify common mistakes students might make.

Answer: {"range":"all real numbers","domain":"(5, ∞)","common_mistakes":["Including x = 5 in the domain","Assuming the range is restricted"]}

Question 9: Extension: Find a quadratic function with vertex at (0, 0), opening upwards, with a domain of all real numbers and a minimum value of 0.

Answer: f(x) = ax^2 where a > 0

Question 10: Challenge: For the function f(x) = (x^3 - 3x + 1), determine the domain and range. Justify your reasoning.

Answer: {"range":"all real numbers","domain":"all real numbers","justification":"Polynomial functions have domain and range of all real numbers due to their continuous nature."}