It is a function if it only touches the vertical line once.
The correct answer is a. for very high x-values, f(x) moves towards positive infinity.
This can always be determined by two factors.
1) is it linear or something else?
2) Is the lead coefficient positive or negative.
In this case, since the x is not being raised to a power or is not raised to a power itself, we know that there are no asymptotes. That takes care of #1 for us.
As for #2, since the coefficient of x (which is the highest power here) is positive, that means it continues to get bigger. If it were negative it would be the opposite. So, the correct answer is that as x gets bigger, f(x) moves towards positive infinity.
That equation would be 1/4x-3<6.
