Final Answer:
The function situation that would have a continuous graph is "The amount of water in a beaker over time."
Step-by-step explanation:
A continuous graph represents a function where the variable changes smoothly and without any abrupt interruptions. In the case of "The amount of water in a beaker over time," the quantity of water is continuously changing as time progresses. This situation lends itself to a continuous graph because, at any given moment, there can be an infinite number of possible water levels in the beaker.
For example, if we denote the amount of water in the beaker as (W) (in milliliters) and time as (t) (in minutes), the relationship could be expressed by a continuous function such as
. This function would yield a smooth curve on a graph, showcasing the changing water level over the continuous flow of time.
In contrast, the other scenarios involve discrete data points or situations where the variables may experience sudden jumps or changes. For instance, the cost for a certain amount of shoes, the number of buses needed for a number of children, and the height of Asia on her birthdays are likely to involve distinct values at specific points rather than a continuous and smooth variation.
In summary, the scenario of "The amount of water in a beaker over time" best fits the criteria for a continuous graph due to the fluid and uninterrupted nature of water level changes over time.