Determine whether or not the equation represents y as a function of x for -y = 2x^4 + 5.

An equation whose variables are x and y represents y as a function of x if it can be manipulated to get a unique* equation with y on one side and an expression on the other side whose only variable is x. (Sometimes the equation is in this form from the beginning, so no manipulation is needed.)
Turning to the equation

we see that while the only variable on the right-hand side is x, the left-hand side is -y rather than y. We can fix this by multiplying both sides of the equation by -1; this gives
.
So the equation does represent y as a function of x.
*To see what we mean by "unique", consider that if our equation was y^2 = x^2, solving for y would give us two different equations with y on one side, namely y=x and y=-x. Because of this, y^2 = x^2 does not represent y as a function of x.


We are asked to determine if -y=2x^4+5 represents y as a function of x.
As written, we have -y written as a function of x, so strictly speaking, the answer is no.
However, if we use algebraic manipulation, we can rewrite y as a function of x. Multiply each side of the equation by the opposite of 1 to get y=-2x^4-5 .
Now f(x)=y=-2x^4-5 is a function of x. For each input of x, there is exactly one output y. (For example, if x=0, then y=-5, if x=1, then y=-7, and so on.) We can also check the graph to determine if it passes the vertical line test—if a graph is the graph of a function, any vertical line will cut the graph in just one place.

Note that many computer algebra systems (graphing calculators and so on) require that a relation be written in function form. In order to graph this function, we need to write the equation as y=-2x^4-5 .
http://mathworld.wolfram.com/Function.html

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