Problem

Given the function \(f(x) = x^3 + 2x^2 - x + 2\), determine if the point \((2,14)\) is on the graph of this function.

Answer

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Answer

Next, compare this y-value to the y-value of the point. If they are the same, then the point is on the graph. Here, \(14 ≠ 16\), so the point \((2,14)\) is not on the graph of the function.

Steps

Step 1 ：First, plug in the x-value of the point into the function to find the corresponding y-value: \(f(2) = 2^3 + 2(2^2) - 2 + 2 = 8 + 8 - 2 + 2 = 16\)

Step 2 ：Next, compare this y-value to the y-value of the point. If they are the same, then the point is on the graph. Here, \(14 ≠ 16\), so the point \((2,14)\) is not on the graph of the function.

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