Imagine water flowing through a pipe into a container. The following equations show how the water level or height of the water (w) in the container was related to the number of minutes (t) when the pipe was opened for 10 minutes.
w = t + 8 for the first four minutes (t = 0 to 4)
w = 3 t for the remaining six minutes (t = 4 to 10)
where w refers to the water level (height) in centimetres, and t refers to the number of minutes. Please use the above information to answer the following questions.
From the given information, do you think the height of the water in the container is increasing at the same rate throughout the 10 minutes? Please show or explain how you obtained your answer.
From the given information, do you think the container already contains water before the pipe was opened? Please state or show how you obtained your answer.
Sketch a possible shape of a container that could fill according to this function.
Beginning students do not recognize the questions as being about slopes and intercepts of graphs of functions. This task can help teachers evaluate the level to which their students understand functions as objects rather than processes.
Students typically evaluate the functions point by point to determine answers rather than looking at the functions holistically.