Determine whether the equation defines y as a function of x

Determine whether the equation defines y as a function of x.

Help please :(

Determine whether the equation defines y as a function of x. 2|x| + y = 0 x = y^3

Solution

65)
2|x| + y = 0

y = 2|x|

We are able to get y completely in terms of x
and notice that y has no even powers

So, this is indeed a function of x

Another way :
Graph it on your calculator
And check if the vertical line test is satisfied.
You will observe that no matter where on the graph you draw a vertical line, it will hit the graph only once
So, vertical line test is satisfied and thus, this is a function

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x = y^3
Can we find y in terms of x?

Yes, y = cuberoot(x)

Since cuberoot has an odd index, this is a function

Also, graph it
The vertical line test would be satisfied

So, this is a function also