is y a function of x?

Question

x^2 + y^2= 4

x^2 + y =4

2x + 3y= 4

y^2=x^2 - 1

im not really sure how 2 do these i know that for every input of x that y can only have 1 output but im still not sure.. plz help

Answer 1

You're correct about the definition of a function: every independent value (x) can have one and only one matching dependent value (y).

x^2 + y^2 = 4 is not a function, because for example when x=0, you could have y=2 or y = -2. On the other hand, x^2 + y = 4 is a function, because even though you can have the same y for two different values of x (for example, (-2,0) and (2,0)), you still have one and only one y value for a given x.

Another way to think about this is to graph the equation. Draw vertical lines on top of it. If one of your lines crosses the graph in two places (which means you'd have two different y values for the same x value), then it's not a function, but rather a relation.

Answer 2

Function Of X

Answer 3

In equations (2) and (3), y is a function of x; simply put y on one side of the equation, and the x-term on the other with any constants. The first and last equations are equations of a circle and hyperola respectively. However, you can still recast them in y=function (x) form. You will see a +/- sqrt(x) term when you do this, and if you treat each part of the+/- as a seperate function, y is a function of x. That gets you "around" the single value restriction.

Answer 4

In the following two, y is a function.
x^2 + y =4
2x + 3y= 4

In the other two, y is not a function.
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Ideas:
If for each x value, you have a unique y value, then it is a function.

Answer 5

y is always a function of x...what are you supposed to solve for?

to put into standard form...Ax + By + C = 0

or slope form......y=mx + b

OH! Geeza is right...I forgot about the circles.

Answer 6

yes, you can write y=f(x) for all those eqn.

not sure , if you wanted to know something else.