A function can be represented by equations and tables
- 4 users are logged in by 9am
- The domain is [3,23] and the range of the function is [3,4]
The number of users at 9am
The function is given as:
[tex]g(x) = \frac14 \sqrt{x - 3} + 3[/tex]
At 9am, x = 9.
So, we have:
[tex]g(x) = \frac14 \sqrt{9 - 3} + 3[/tex]
[tex]g(x) = \frac14 \sqrt{6} + 3[/tex]
Simplify
[tex]g(9) = 3.6[/tex]
Approximate
[tex]g(9) = 4[/tex]
Hence, 4 users are logged in by 9am
The domain
Set the radical to 0
[tex]x - 3 = 0[/tex]
Solve for x
[tex]x = 3[/tex]
The maximum time after midnight is 23 hours.
So, the domain is [3,23]
The range
When x = 3, we have:
[tex]g(x) = \frac14 \sqrt{x - 3} + 3[/tex]
[tex]g(3) = \frac 14 * \sqrt{3 - 3} + 3 = 3[/tex]
When x = 23, we have:
[tex]g(23) = \frac 14 * \sqrt{23 - 3} + 3 = 4[/tex]
So, the range of the function is [3,4]
Read more about domain and range at:
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