Question

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

Answer 1

Answers:

• A) No, it is not a function
• B) Yes it's a function
• C) Not a function
• D) Yes it's a function
• E) Yes it's a function

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Explanation:

If y has an exponent of 2, 4, 6, etc (basically any even number) then it leads to having inputs with multiple outputs.

Consider something like y^2 = x. If x = 100, then y = 10 or y = -10 are possible. A function can only have exactly one y output for any valid x input. Similar issues happen for things like y^4 = x and so on. So this is why A and C are not functions.

The other equations do not have y values with such exponents, so we can solve for y and have each x input lead to exactly one y output. Therefore, they are functions.