#6 AAE Polynomial Functions

What is the maximum number of turning points for the graph of this polynomial function?

 $f(x)=2x^5-3x^2+4x-10$  

• 5

• 4

• 3

• 2

• 1

• 5

• 4

• 3

• 2

• 1

The polynomial function will cross the y-axis at which point?


 $f(x)=2x^5-3x^2+4x-10$  

• (-2, 0)

• (0, -2)

• (-10, 0)

• (0, -10)

Choose the end behavior for this polynomial function.

 $f(x)=2x^5-3x^2+4x-10$  

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

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

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

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

What would be the minimum degree of the polynomial based on the graph shown and why?

• 4th degree polynomial determined by the graphs end behavior.

• 4th degree polynomial because the graph crosses or touches the x-axis 4 times.

• 5th degree polynomial because the graph has 5 hills and valleys.

• 6th degree polynomial determined by the number of zeros and end behavior of the graph.

What are the zeros and their multiplicities of the polynomial graphed?

• -6 (multiplicity of 1)

  -5 (multiplicity of 2)

  -2 (multiplicity of 2)

  1 (multiplicity of 1)

• -6 (multiplicity of 2)

  -5 (multiplicity of 1)

  -2 (multiplicity of 1)

  1 (multiplicity of 2)

• 6 (multiplicity of 1)

  5 (multiplicity of 2)

  2 (multiplicity of 2)

  -1 (multiplicity of 1)

• 6 (multiplicity of 2)

  5 (multiplicity of 1)

  2 (multiplicity of 1)

  -1 (multiplicity of 2)

The Rational Zeros Theorem states  $\frac{p}{q}$   is a rational zero of  $f\left(x\right)$   if  $p$   is a factor of the constant term and  $q$  is a factor of the leading coefficient . Is -3 a possible rational zero for the polynomial  $f\left(x\right)$ ?  $f\left(x\right)=5x^4+8x^2-7x+15$  Why or why not?

• Yes, because 3 is a factor of p, the constant term of the polynomial. 

• Yes, because 3 is a factor of q, the leading coefficient.

• No, because 3 is not a factor of p, the constant term of the polynomial. 

• No, because 3 is not a factor of q, the leading coefficient.

Using the Rational Zeros Theorem, which is the complete list of the possible rational zeros for the polynomial function?

 $f\left(x\right)=5x^4+8x^2-7x+15$  

•  $\pm1,\ \pm3,\ \pm5,\ \pm15$  

•  $\pm\frac{1}{5},\ \pm1,\ \pm\frac{3}{5},\ \pm3,\ \pm5,\ \pm15$ 

•  $\pm\frac{1}{15}\pm\frac{1}{5}\pm\frac{1}{3}\pm1,\ \pm\frac{5}{3},\ \pm3\pm5$ 

•  $\pm\frac{1}{15}\pm\frac{1}{5}\pm\frac{1}{3}\pm1,\ \pm\frac{5}{3}\pm5,\ \pm15$  

Tags

CCSS.HSA.APR.B.2

At the root  $x=-1$  on  $f\left(x\right)\ =\ \left(3x+3\right)^7\left(6x-6\right)^2\left(x^2+1\right)$  the graph...

• Touches or bounces off of the y-axis like a parabola

• Crosses or passes through the y-axis like a line

• Touches or bounces off of the x-axis like a parabola

• Crosses or passes through the x-axis like a line

There are 2 ways to tell if   $\left(x+5\right)$  a factor of  $f\left(x\right)=\ -x^4-25x^2$ 

Select the 2 ways below.

• No, the function has a remainder of -30 when I synthetically divide by 5.

• No, the function has a remainder of -20 when I synthetically divide by -5. 

• No, the function has a remainder of -1250 when I synthetically divide by -5

• No, because the function equals -1250 when I substitute -5 in for x. 

Tags

CCSS.HSA.APR.B.2