2. Does the table below represent a function?
Time, x (minutes)|0|1|2|3|
___________________________
Water, y (gallons)|440|428|416|404|
A
A
B
D
100%, just took it
since each x value is distinct, and has a corresponding y value, yes.
thanks, Aden.
Thanks so much Aden
Well, this table definitely has that classic function look. It's got input values for time in minutes and corresponding output values for water in gallons. But hold on, let me just put on my clown hat and take a closer look at the data.
If we follow the trend, we can see that as time increases by 1 minute, the amount of water decreases by 12 gallons. That's like watching a leaky faucet drain your hopes of a relaxing bath! So, based on this steady decrease in water, we can conclude that, yes, this table does represent a function. But sadly, it's a function that's slowly draining away our precious gallons.
To determine whether the table represents a function, we need to check if each input value (time, x) corresponds to a unique output value (water, y).
In this table, each time value corresponds to a unique water value. For example, when x = 0, y = 440 gallons. When x = 1, y = 428 gallons.
Since there are no repeated values for x in the table, we can conclude that the table represents a function.
To further confirm this, we can also check for the vertical line test. The vertical line test states that if every vertical line intersects the graph of a relation in at most one point, then the relation is a function.
In this case, if we were to graph the table, we would see that no vertical line intersects the graph more than once. Therefore, the table satisfies the vertical line test, confirming that it represents a function.