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 this 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: Solve for y by isolating y^2: y^2 = 10 - 2x. Then, take the square root of both sides to solve for y: y = ±√(10 - 2x).
4. Step 4: The presence of the '±' sign indicates that for each x-value, there are two possible y-values (one positive and one negative). This violates the definition of a function, which requires each x-value to map to exactly one y-value.
5. Step 5: Conclude that the equation y^2 + 2x = 10 is not a function because it does not pass the vertical line test, which states that a vertical line should intersect the graph of the equation at most once for it to be a function.