Casey ran a 75 meter race in 10 seconds her distances at certain times during the race are shown in the table . what is the domain for the graph of the function that would model her race[ time in seconds 0 1 2 3 4 5 6 7 8 9 10 : distance in meters 0.0 5.5 12.0 20.0 28.5 36.0 44.0 56.5 64.0 75.0

The domain of the graph is everything x is allowed to equal. Parentheses are used to show that x can be everything up to, but not including that number. Brackets are used to show x can be anything up to, and including, that number. The comma between the two numbers indicates that x can be anything between those two numbers.

Here, the time goes on the x axis and the distance will go on the y axis.
Time: 0 1 2 3 4 5 6 7 8 9 10
Distance: 0.0 5.5 12.0 20.0 28.5 36.0 44.0 56.5 64.0 75.0

Since we are dealing with the domain, we really only need to focus on the time.
Time: 0 1 2 3 4 5 6 7 8 9 10

From this, we see that the values go from 0 to 10. This means that x can be anything from 0 to 10. Because there are y values that correlate with the numbers 0 and 10, we know that the domain will include 0 and 10. This indicates we must use brackets. 

Knowing all of this information, we can now write our domain as:
[0, 10]