Question

Examine the graph below.A coordinate plane is scaled from negative 5 to 5 in increments of 1 on the x-axis and from negative 5 to 5 in increments of 1 on the y-axis. A curve starts at around (negative 4, 2) and decreases to about (negative 2, negative 3.5) then increases to about (negative 1, 2) before decreasing to about (2, negative 4) and then increasing to the top right of the graph.Which of the following statements is NOT true regarding the polynomial whose graph is shown?The degree of the polynomial is even.The leading coefficient is positive.The function is a second-degree polynomial.As x→±∞,y→∞.

Answer 1

*The degree of the polynomial is even.

This is true since the graph crosses the x-axis 4 times, since 4 is even, we can conclude it is true.

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*The leading coefficient is positive.

This is true since:

`\begin{gathered} \lim _(x\to\infty)f(x)=\infty \\ \lim _(x\to-\infty)f(x)=-\infty \end{gathered}`

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*As x→±∞,y→∞.

This is true because of the previous reason

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*The function is a second-degree polynomial.

This is false, the polynomial is 4th-degree

Answer:

The function is a second-degree polynomial.