Question

(20 pts)

Answer 1

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:

$g(x) = \frac14 \sqrt{x - 3} + 3$

At 9am, x = 9.

So, we have:

$g(x) = \frac14 \sqrt{9 - 3} + 3$

$g(x) = \frac14 \sqrt{6} + 3$

Simplify

$g(9) = 3.6$

Approximate

$g(9) = 4$

Hence, 4 users are logged in by 9am

The domain

Set the radical to 0

$x - 3 = 0$

Solve for x

$x = 3$

The maximum time after midnight is 23 hours.

So, the domain is [3,23]

The range

When x = 3, we have:

$g(x) = \frac14 \sqrt{x - 3} + 3$

$g(3) = \frac 14 * \sqrt{3 - 3} + 3 = 3$

When x = 23, we have:

$g(23) = \frac 14 * \sqrt{23 - 3} + 3 = 4$

So, the range of the function is [3,4]

Read more about domain and range at:

brainly.com/question/2264373