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題目

解題步驟

1. Understand the question

   which of the following are polynomial functions?

2. Explanation

   Step1: Recall polynomial graph rules

   Polynomial functions have smooth, unbroken graphs with no sharp corners or horizontal line segments (constant slope sections that are not part of a smooth curve).

   Step2: Analyze first graph

   The first graph has a sharp corner at the origin, so it is not a polynomial (this is the graph of $y=|x|$, an absolute value function, not a polynomial).

   Step3: Analyze second graph

   The second graph is smooth, continuous, with no sharp corners or flat segments that break smoothness. This fits the shape of a cubic or higher-degree polynomial, so it is a polynomial function.

   Step4: Analyze third graph

   The third graph is a smooth, downward-opening parabola ($y=-ax^2 + b$, $a>0$), which is a 2nd-degree polynomial. It has no sharp corners or breaks, so it is a polynomial function.

   Step5: Analyze fourth graph

   The fourth graph has a horizontal flat segment, which creates a non-smooth transition (not a continuously differentiable curve everywhere, which polynomials are). This is not a polynomial function.

3. Final answer

   The second graph (smooth, rising/falling curve with a local max and min) and the third graph (downward-opening parabola) are polynomial functions.

答案

Question Analysis

OCR Text

which of the following are polynomial functions?

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