Question 1: Determine the domain and range of the function y = 3x + 2.

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

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

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

Question 3: A function models the height of a ball in meters over time in seconds. The graph shows the height reaches a maximum at 4 seconds and then decreases. What can you infer about the domain and range of this function?

Answer: {"range":"from 0 meters up to maximum height","domain":"from 0 to 4 seconds"}

Question 4: Construct a triangle on the grid with side lengths corresponding to a function with domain [1, 5] and range [2, 8].

Answer: {"description":"Triangle with sides of lengths 4, 6, and 8, positioned within the grid to reflect the specified domain and range."}

Question 5: The function f(x) = √x is defined for x ≥ 0. What is the domain and range of this function? Explain your reasoning.

Answer: {"range":"y ≥ 0 (all non-negative real numbers)","domain":"x ≥ 0 (all non-negative real numbers)"}

Question 6: A car's speed in km/h over time (hours) is modeled by the function v(t) = -2t + 60. Find the domain and range, and explain what they represent in this context.

Answer: {"range":"0 ≤ v ≤ 60 km/h","domain":"0 ≤ t ≤ 30","explanation":"Time from start until the car stops, and speed decreasing over time until it reaches zero."}

Question 7: Identify and correct the mistake: The function y = 1/(x - 3) has domain all real numbers.

Answer: The domain excludes x = 3, because division by zero is undefined.

Question 8: A rollercoaster's height in meters after t seconds is given by h(t) = -4t² + 20t + 5. Determine the domain and range of h(t), and interpret their meanings.

Answer: {"range":"from 5 meters up to maximum height (at t=2.5 seconds)","domain":"0 ≤ t ≤ 5 seconds (time during ascent and descent)"}

Question 9: Given the function f(x) = log(x), find the domain and range, and justify your answer.

Answer: {"range":"all real numbers","domain":"x > 0"}

Question 10: A water tank's volume V in litres is given by V = 50x, where x is the height in meters. What is the domain and range of this function if the height x can only be between 0 and 3 meters?

Answer: {"range":"0 ≤ V ≤ 150 litres","domain":"0 ≤ x ≤ 3"}

Question 11: Explain why the domain of the function y = √(x - 1) is x ≥ 1, and what this implies about the possible input values.

Answer: Because the expression under the square root must be non-negative (≥ 0), so x - 1 ≥ 0, meaning x ≥ 1.