Question

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?

Answer 1

Hmm.. @Zenia \(\color{blue}{\huge\tt{Welcome~}}\) \(\huge\mathcal{to}\) \(\color{red}{\huge\tt{Open~Study~!}}\)

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]

\(\color{blue}{\huge\tt{Nice~}}\) \(\huge\mathcal{to~meet~}\) \(\color{red}{\huge\tt{You~!}}\)