Sovi AI

Question

Solution Steps

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.

Answer

Question Analysis

OCR Text

which of the following are polynomial functions?

Related Topics

Related Questions

• use an area model to solve 31 × 26. multiply in the area model.

  Top-left cell: 180 Top-right cell: 6 Bottom-left cell: 600 Bottom-right cell: 20 Final product: 806

• 6. solve each equation. write each solution as a fraction and as a deci…

  | Equation | Solution (Fraction) | Solution (Decimal) | |----------|---------------------|--------------------| | $2x=3$ | $\frac{3}{2}$ | $1.5$ | | $5y=3$ | $\frac{3}{5}$ | $0.6$…

• Ok

  - Fila 2: Circular el par (5, 2). - Fila 3: Circular el par (3, 3) (o la tarjeta con 3 y la otra con 4 dibujos, pero los números son 3 y 3? Wait, la tercera fila: primera tarjeta …

• How do you solve pemdas

  It's basically just a checklist so you don't get mixed up when a math problem has a bunch of stuff going on at once. You just go down the list in order: 1. **P**arentheses: Do any…

• which number line models $-1 + (-14)$? add. $-1 + (-14) = \\square$

  \(-15\)

• 11 et 12

  The initial number of bacteria is 5. ### Turn 2 Answer Ça marche, regardons ça ! On dirait que tu es en plein dans les maths financières. Pour le **numéro 11**, on cherche le taux…

• use the graph of the polynomial function shown below to identify the ze…

  | Zeros | Mult. | |-------|-------| | $-4$ | $3$ | | $0$ | $1$ | | $4$ | $2$ | | | |

• question 8 use the graph of the polynomial function shown below to iden…

  | Zeros | Mult. | |-------|-------| | $-7$ | $2$ | | $1$ | $1$ | | $6$ | $1$ |

Sovi AI iOS

Official website: mysovi.ai. Question pages are served on question-banks.mysovi.ai. iOS app is distributed through the Apple App Store.