transformation problem 2: 4 - y = sqrt(3x) is moved 9 up, reflected in x-axis

[khorven]

The function 4 - y = square root (3x) is translated 9 units up and reflected in the x-axis. Without graphing, determine the domain and range of the image function.

In the answers section, it shows the range as y >= -13. I don't understand why it's negative and not positive 13.

 

[ksdhart]

You're given the function 4 - y = sqrt(3x). What if you rearrange it so that it's a function y = (something)? That rewritten function is then translated 9 units up. So what does the new function look like? Now you need to reflect the function over the x-axis. Remember that when reflecting about the x-axis, y = f(x) becomes y = -f(x). So, what is your final function after translating and reflecting? And what's the range of that function?

 

[khorven]

y = -sqrt(3x) + 4

y = -sqrt(3x) + 13

y = sqrt(3x) - 13

y >= -13

In my textbook it says translate after reflections/stretches. So is this how it would look if you translated before reflecting? Did I get this right?