Given xy+6y=1. Is y a function of x?

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Yes, y is a function of x because when you will graph this equation there will not be 2 y values in 1 x value. Example, (1,2) x=1 and y=2 and (1,4) x=1 and y=4. In both of these the value of x stays 1 but y is 2 and 4. If this happens so y will not be the function of x. In this equation this does not happens so y is a function of x. Hope this helped.

yes. y is a function of x

For an equation to be a function, you can only get one output (y) for any input (x). Now let's test. Create fast table of values using 5 sample inputs (x's) like -2,-1,0,1, 2. Put each x into the equation and solve for y. Use the ordered pairs to sketch a graph.Now apply the vertical line test. If a vertical line drawn anywhere can intersect your graphed line at only one point, you have a function  Each x you put in resulted in a unique y output! Good Luck.