6.1 Attributes of Polynomial Functions

Which of the following statements is false about the graph of the polynomial function given?

• The function passes through the origin.

• The function has a zero at -3.

• The function has a local maximum at (-1.76, -3.46).

• The function has an x-intercept at (3,0).

A polynomial function, P(x), is shown on the grid. Which of the following statements is false about the graph of P(x)?

• P(x) has a local minimum at (-3,-2).

• P(x) has a root of -5.

• P(x) has a global maximum at (3, 2).

• P(x) has an x-intercept at (5,0).

The graph of a polynomial function is shown on the grid. Which of the following statements about the function is false?

• The function has a global minimum at (2.2, -2.8).

• The function has a global maximum at (-0.2,2.1).

• The function has a local minimum at (-2,0).

• The graph has y-intercept at (0,2).

What is the degree of the polynomial function  $f\left(x\right)=-5x^7+4x^6-3x^4-11x^2+6$  ?

• -5

• 5

• 7

• -11

What is the degree of the polynomial function  $g\left(x\right)=2x^3+4x^5-7x^2+1$  ?

• 5

• 3

• -7

• 4

What is the degree of the function  $f\left(x\right)=x\left(x+3\right)\left(x-4\right)$  ?

• 1

• 2

• 3

• 4

Which of the following best describes the end behavior of the polynomial function,  $f\left(x\right)$  , shown in the graph?

•  $\lim_{x\rightarrow-\infty}f\left(x\right)=\infty$  and  $\lim_{x\rightarrow\infty}f\left(x\right)=\infty$  
  
  

•  $\lim_{x\rightarrow-\infty}f\left(x\right)=\infty$   and  $\lim_{x\rightarrow\infty}f\left(x\right)=-\infty$  

•  $\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$  and  $\lim_{x\rightarrow\infty}f\left(x\right)=\infty$  

•  $\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$  and  $\lim_{x\rightarrow\infty}f\left(x\right)=-\infty$  

Which of the following best describes the end behavior of the polynomial function, $f\left(x\right)$ , shown in the graph?

• $\lim_{x\rightarrow-\infty}f\left(x\right)=\infty$ and $\lim_{x\rightarrow\infty}f\left(x\right)=\infty$
  
  

• $\lim_{x\rightarrow-\infty}f\left(x\right)=\infty$ and $\lim_{x\rightarrow\infty}f\left(x\right)=-\infty$

• $\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$ and $\lim_{x\rightarrow\infty}f\left(x\right)=\infty$

• $\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$ and $\lim_{x\rightarrow\infty}f\left(x\right)=-\infty$

Which of the following best describes the end behavior of the polynomial function, $f\left(x\right)$ , shown in the graph?

• $\lim_{x\rightarrow-\infty}f\left(x\right)=\infty$ and $\lim_{x\rightarrow\infty}f\left(x\right)=\infty$
  
  

• $\lim_{x\rightarrow-\infty}f\left(x\right)=\infty$ and $\lim_{x\rightarrow\infty}f\left(x\right)=-\infty$

• $\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$ and $\lim_{x\rightarrow\infty}f\left(x\right)=\infty$

• $\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$ and $\lim_{x\rightarrow\infty}f\left(x\right)=-\infty$

Which statement below describes the degree and sign of the leading coefficient of the polynomial function shown in the graph?

• An even degree with a positive leading coefficient.

• An even degree with a negative leading coefficient.

• An odd degree with a positive leading coefficient.

• An odd degree with a negative leading coefficient.