Julie S. answered • 08/30/18
Tutor
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Chemistry Can Be Fun! 25 Years Tutoring Gen Chem and Orgo Chem
Adriane - I see you asked three similar questions... Do you know the definition of a function? To put it loosely, we can say that "y is a function of x" if (and only if) each input for x gives only one output for y.
So pick a number for x, put it into the equation and solve for y. Does it give you ONE answer?
Pick another number for x, put it in and solve for y. Does it give you ONE answer?
Pick a whole bunch of numbers for x, a variety of types - pick x = 0, x = a small number, x = a large number, x = a negative number... Do you always get ONE answer when you plug them in?
If the answer is yes, then you should have an equation where y is a function of x.
For this one if we put in x = 0 then y =1. y does not also equal something else sometimes when x = 0, that is the ONLY value that y can have, right?
If we put in x = 1, then y = 2. Again, we get only one result here. Keep checking, and you will not be able to find any numbers you can put in for x that give you more than one result for y.
If we had the equation y = √x, then we could say that when x = 4, y might be 2 or it might be -2! Both answers work... Therefore for this equation we would say that y is NOT a function of x, because one x input gives us 2 different y outputs! Hope that helps...
