5.3 Polynomial Graphs Review of Notes

5.3 Polynomial Graphs Review of Notes

Please use this lesson as an opportunity to review your notes from 5.3.

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When you finish this assignment, work on the practice problems 1-10 in the 5.3 Packet. ​

5.3 Review of Notes

• Features of polynomial graphs

• End behavior of polynomial functions

• Turning points, zeros and multiplicity

Multiple Choice

Which of the following is the graph of a polynomial function?

Multiple Choice

Which of the following is the graph of a polynomial function?

Multiple Select

 What is the end behavior of the equation given below (you need to make two choices for x approaches infinity, and x approaches negative infinity).

$$f\left(x\right)=-4x^3+5x^2-7x+11$$

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

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

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

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

Multiple Select

What is the end behavior of the equation given below (you need to make two choices for x approaches infinity, and x approaches negative infinity).

$$f\left(x\right)=5x^6-7x^3+14x-9$$

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

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

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

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

Multiple Select

What is the end behavior of the equation given below (you need to make two choices for x approaches infinity, and x approaches negative infinity).

$$f\left(x\right)=-\frac{1}{2}x^2+19x-29$$

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

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

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

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

Multiple Select

What is the end behavior of the equation given below (you need to make two choices for x approaches infinity, and x approaches negative infinity).

$$f\left(x\right)=4x^7-4x^4+12x^2-10$$

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

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

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

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

Fill in the Blank

At most, how many turning points (extrema) does the polynomial below have?

$$f\left(x\right)=3x^4-2x^2+9$$  

Multiple Choice

Which polynomial below could have at most 4 turning points (extrema)?

• $$f\left(x\right)=x^5-3x^3+2x-9$$

• $$f\left(x\right)=4x^3+2x^2-5x-10$$

• $$f\left(x\right)=x^4+12x^2-7x+14$$

Multiple Choice

Which of the polynomials below *could* have at most 6 zeros?

• $$f\left(x\right)=4x^4-5x^2-14$$

• $$f\left(x\right)=-2x^6+4x^4-3x^2+2x-9$$

• $$f\left(x\right)=3x^5-4x^3+2x-9$$

Fill in the Blank

At most, how many zeros does the polynomial below have?

$$f\left(x\right)=5x^4-7x^2+1$$  

Multiple Select

 Given the polynomial $$f\left(x\right)=x^3\left(x-2\right)^2\left(x-5\right)^5\left(x+3\right)^8$$ which of the following zeros are CROSSING the x-axis (select all that apply. 

• 0
  

• 2

• 5

• -3

Multiple Select

 Given the polynomial $$f\left(x\right)=x^3\left(x-2\right)^2\left(x-5\right)^5\left(x+3\right)^8$$ which of the following zeros are TANGENT to the x-axis (select all that apply. 

• 0
  

• 2

• -5

• -3

Fill in the Blank

According to Decart's rule of signs, what is the MOST amount of positive real zeros you will find in the equation below?

$$f\left(x\right)=27x^9-x^6-27x^3+1$$  

Fill in the Blank

According to Decart's rule of signs, what is the MOST amount of negative real zeros you will find in the equation below?

$$f\left(x\right)=27x^9-x^6-27x^3+1$$