Is the equation $y^2+2x=10$ a function? If so, rewrite it in function notation and evaluate at $f\left(-1\right)$.

• A. $f\left(-1\right)=\sqrt{12}$, Is A Function
• B. $f\left(-1\right)=12$, Is A Function
• C. $f\left(-1\right)=\frac92$, Is A Function
• D. Is NOT A Function

Answer: (D)

Verified step by step guidance

1. Step 1: Begin by examining the given equation y^2 + 2x = 10. To determine if this is a function, recall that a function must have only one output (y-value) for each input (x-value).
2. Step 2: Consider the equation y^2 + 2x = 10. Rearrange it to isolate y^2: y^2 = 10 - 2x.
3. Step 3: Notice that y^2 = 10 - 2x implies y = ±√(10 - 2x). This indicates that for each x-value, there are potentially two y-values (one positive and one negative), which violates the definition of a function.
4. Step 4: Since the equation y^2 + 2x = 10 can produce more than one y-value for a given x-value, it is not a function.
5. Step 5: Therefore, the equation y^2 + 2x = 10 is not a function, and it cannot be rewritten in function notation or evaluated at f(-1).