Determine whether −9x−3y2=6 represents a function of x.

No (not a function of x)

Step-by-step explanation:

Begin by isolating the y-term to find

−9x−3y2−3y2y2=6=9x+6=−3x−2

For each value of x, multiply it by −3, add −2, and then take the square root to get the y-value. For example, if x=−6, we have

y2y2y2y=4=−3x−2=−3(−6)−2=16ory=−4

We have that if x=−6, then y=4 or y=−4. In other words, a single value of x results in more than one value of y. Since some value of x corresponds to more than one value of y, the equation does not define a function.

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