The correct function is [tex]y = - \sqrt{x - 6} [/tex]
How to find the correct function?
A rational function is a function that can be written in fraction form.
from the question, to choose the function for which [tex]y → - \infty \: and \: x→ \infty [/tex]
so take the function and substitute [tex]y = - \infty [/tex]into the function.
[tex]y = - \sqrt{x - 6} [/tex]
[tex] - \infty = - \sqrt{x - 6} \\ \infty = \sqrt{x - 6} \\ \infty = x - 6 \\ \infty + 6 = x \\ x = \infty [/tex]
Hence the correct function is [tex]y = - \sqrt{x - 6} [/tex]
Learn more about fractions, refer:
https://brainly.in/question/436067
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