Question

The function g(x)=1/4 3√x-3+2 represents, in millions, the number of users who have logged into a website since midnight.

Answer 1

A function can be represented by equations and tables

• 3 million users are logged in by 9am
• The transformation is: 2 units shift down, 3 units left and vertical stretch by a factor of 4

The number of users at 9am

The function is given as:

$g(x) = \frac14 \sqrt{x - 3} + 2$

At 9am, x = 9.

So, we have:

$g(x) = \frac14 \sqrt{9 - 3} + 2$

$g(x) = \frac14 \sqrt{6} + 2$

Simplify

$g(9) = 2.6$

Approximate

$g(9) = 3$

Hence, 3 million users are logged in by 9am

The transformation to f(x)

We have:

$g(x) = \frac14 \sqrt{x - 3} + 2$

Translate the function 2 units down

So, we have:

$g'(x) = \frac 14\sqrt{x -3}$

Translate the function 3 units left

$g"(x) = \frac14 \sqrt x$

Stretch vertically by 4

$f(x) = \sqrt x$

Hence, the transformation is:

2 units shift down, 3 units left and vertical stretch by a factor of 4

Read more about function transformation at:

brainly.com/question/1548871