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: Start by analyzing the given equation y^2 + 2x = 10. To determine if it is a function, we need to check if for every x-value there is only one corresponding y-value.
2. Step 2: Rearrange the equation to express y in terms of x. This involves isolating y on one side of the equation. However, notice that y is squared, which suggests that for some x-values, there might be two possible y-values (one positive and one negative).
3. Step 3: Consider the definition of a function: a relation where each input (x-value) has exactly one output (y-value). If solving for y results in more than one value for a single x, then the equation is not a function.
4. Step 4: Attempt to solve for y by isolating y^2: y^2 = 10 - 2x. Taking the square root of both sides gives y = ±√(10 - 2x). The presence of the '±' indicates two possible y-values for each x, confirming it is not a function.
5. Step 5: Since the equation does not satisfy the definition of a function, it cannot be rewritten in function notation, and evaluating it at f(-1) is not applicable. Therefore, the equation is not a function.