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You are watching: Determine whether the equation represents y as a function of x

We are asked to identify if `-y=2x^4+5 ` represents y as a duty of x.

**As written, we have actually -y composed as a function of x, so strictly speaking, the answer is no.**

However, if we use algebraic manipulation, we deserve to recompose y as a function of x. Multiply each...

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We are asked to determine if `-y=2x^4+5 ` represents y as a duty of x.

**As composed, we have actually -y created as a role of x, so strictly speaking, the answer is no.**

However before, if we use algebraic manipulation, we have the right to rewrite y as a duty of x. Multiply each side of the equation by the oppowebsite of 1 to get `y=-2x^4-5 `.

Now `f(x)=y=-2x^4-5 ` is a duty of x. For each input of x, tright here is precisely one output y. (For instance, if x=0, then y=-5, if x=1, then y=-7, and also 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 duty, any type of vertical line will cut the graph in simply one location.

Note that many computer system algebra devices (graphing calculators and also so on) require that a relation be written in function develop. In order to graph this feature, we should create the equation as `y=-2x^4-5 `.

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