Question

is this function discrete or continuous? how do you know?
continuous, because it’s a connected line with no breaks
discrete, because it ends
discrete, because it isn’t a straight line
continuous, because it keeps going

Explanation:

To determine if a function is discrete or continuous, we analyze the graph:

• A discrete function has isolated points (not connected).
• A continuous function has a connected graph with no breaks, representing data that can take any value in an interval (e.g., time, temperature).

The graph here is a connected line (no breaks) showing temperature over time (hours since midnight). Time and temperature are continuous quantities (they can take any value in a range, not just whole numbers). The yellow option correctly states it is continuous because the graph is a connected line with no breaks.

Other options are incorrect:

• "discrete, because it ends": A graph ending does not make it discrete (discrete depends on connectedness, not length).
• "discrete, because it isn’t a straight line": Linearity is irrelevant to discrete/continuous classification.
• "continuous, because it keeps going": The graph may end, but "keeps going" is not the key; the key is the connected, unbroken line.

Answer:

A. continuous, because it’s a connected line with no breaks