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Multiple Choice
Is the equation y2+2x=10 a function? If so, rewrite it in function notation and evaluate at f(−1).
A
f(−1)=12, Is A Function
B
f(−1)=12, Is A Function
C
f(−1)=29, Is A Function
D
Is NOT A Function
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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.
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).
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).
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.
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.