Question

Determine if the following relations represent y as a function of x.

Answer 1

Answers:

• A) yes
• B) yes
• C) yes
• D) no

Each yes/no answer refers to the question "is this a function?"

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Explanation:

The last equation is not a function because of the even exponent over the y term. If you apply the fourth root to both sides, you'll end up with y = |x| and y = -|x| as the two possibilities. For any nonzero x, there are multiple y outputs.

The first three equations are functions because we don't have the same issue as the last equation. All exponents for the y terms are odd. Something like y without an exponent really means y^1.