Question 1: Given the function f(x) = 3x + 2, find the domain and range.

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

Question 2: Plot the graph of y = 2x on the grid. Describe the domain and range.

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

Question 3: For the function f(x) = √x, state the domain and range.

Answer: {"range":"f(x) ≥ 0","domain":"x ≥ 0"}

Question 4: Construct a triangle with vertices at (0,0), (x, y), and (x + 3, y + 4). What are the possible domain and range values for x and y if the triangle must fit within a 10 by 10 grid?

Answer: {"range":"dependent on x and y, within grid limits","domain":"x between 0 and 7, y between 0 and 6"}

Question 5: Given f(x) = 1/(x - 1), identify the domain and range, noting any restrictions.

Answer: {"range":"all real numbers except y ≠ undefined at x=1","domain":"x ≠ 1"}

Question 6: Determine the domain and range of the quadratic function f(x) = x² - 4x + 3.

Answer: {"range":"y ≥ -1","domain":"all real numbers"}

Question 7: Explain why the function f(x) = log(x) has a restricted domain, and specify it.

Answer: {"explanation":"Because the logarithm is only defined for positive x, so domain is x > 0."}

Question 8: The function f(x) = |x - 3|. What are the domain and range?

Answer: {"range":"y ≥ 0","domain":"all real numbers"}

Question 9: Identify the domain and range of the function f(x) = (2x + 1)/(x - 2).

Answer: {"range":"all real numbers except y is undefined at x=2","domain":"x ≠ 2"}

Question 10: A real-world scenario: The height h(t) in meters of a ball thrown vertically is given by h(t) = -4.9t² + 10t. What are the possible domain and range values for t?

Answer: {"range":"h(t) between 0 and 5.1 meters","domain":"t ≥ 0"}

Question 11: Identify the domain and range of the piecewise function: f(x) = {x + 2 for x ≤ 3, 5 for x > 3}.

Answer: {"range":"y ≥ 2","domain":"all real numbers"}

Question 12: A student incorrectly states that the domain of f(x) = √x is all real numbers. Explain the mistake and correct it.

Answer: {"mistake":"Incorrectly assumes √x is defined for negative x.","correction":"The domain is x ≥ 0, since square root of negative numbers is undefined in real numbers."}