POLYNOMIAL FUNCTIONS (REVIEW)

POLYNOMIAL FUNCTIONS (REVIEW)

To be done before taking the QUIZ!

LOCAL MINIMUM AND MAXIMUM

These are the turning points of the graph. Local Maximum if it is opening downward and local minimum if opening upward. These local min and max are also called TURNING POINTS. The degree of the polynomial minus one tells you the number of turning points. Example: If the degree of the polynomial is 5, then the graph have at most 5 turning points.

We can have the coordinates of these local max and min using DESMOS calculator or TI 84.

Multiple Choice

How many turning points are there in the function:

 $f\left(x\right)\ =\ 2x^4-3x^{ }$  

• 4

• 3

• 2

• 1

Degree, Leading Term and Leading Coefficient

The degree of a polynomial is the highest power of the said polynomial. If the powers are not arranged, look for the highest exponent.

Leading term is the term having the highest exponent.

Leading Coefficient is the constant (number) in the leading term.

Example 1:  $f\left(x\right)\ =\ 3x^6-\ 2x^5-x^{4\ }+2x\ -3$  



Example 2:  $f\left(x\right)\ =\ 6x^2-3x^5+2x\ -1$  

Multiple Choice

What is the degree of the polynomial?

 $f\left(x\right)\ =\ 2x^4-3x^2-2x\ -4?$  

• 4

• 3

• 2

• 1

Multiple Choice

What is the leading term of the polynomial?

 $f\left(x\right)\ =\ 3x^3-6x^5-2x^2-5\ ?$  

•  $3x^3$  

•  $-6x^5$  

•  $-2x^2$  

• -5

Even and Odd Degree Polynomials

• EVEN DEGREE ---Both arrows are in the same direction. They point up if the leading coefficient is positive and down id the leading coefficient is negative.

• ODD DEGREE--- Arrows are having opposite direction. One is pointing up and one is pointing down. The lead coefficient is positive if the graph is going up if you trace them from left to right.

Multiple Select

Check all the even degree polynomials:

END BEHAVIOR

• Watch the video to review.

Multiple Choice

What of the following is a correct end behavior?

• 
  

   $as\ x\ \longrightarrow\infty,\ f\left(x\right)\longrightarrow\ \infty\$  
  

•  $as\ x\ \longrightarrow\infty,\ f\left(x\right)\longrightarrow-\infty$  

Multiple Choice

What of the following is a correct end behavior?

• 
  

   $as\ x\ \longrightarrow-\infty,\ f\left(x\right)\longrightarrow\ \infty\$  
  

•  $as\ x\ \longrightarrow-\infty,\ f\left(x\right)\longrightarrow-\infty$  

DOMAIN AND RANGE

• ODD DEGREE POLYNOMIALS

Multiple Choice

What is the domain and range of the polynomial?

 $f\left(x\right)\ =\ 3x^{7\ }-\ 2x^{4\ }-\ 3x\ +1$  

•  $D\left(-\infty,\ \infty\right)\ R\left(1,\ \infty\right)$  

•  $D\left(-\infty,\ \infty\right)\ R\left(2,\ \infty\right)$  

•  $D\left(1,\ \infty\right)\ R\left(-\infty,\ \infty\right)$  

•  $D\left(-\infty,\ \infty\right)\ R\left(-\infty,\ \infty\right)$  

DOMAIN AND RANGE

• EVEN DEGREE POLYNOMIALS

• 
  

Multiple Choice

What is the domain of the graph?

• $\left(-\infty,\ \infty\right)$

• $\left(\infty,\ 1\right)$

• $\left(1,\ \infty\right)$

• Cannot be determined.

Multiple Choice

What is the range of the function?

• $\left(-\infty,\ \infty\right)$

• $\left(-1,\ \infty\right)$

• $\left(-\infty,\ -1\right)$

• $\left(\infty,\ -1\right)$

INCREASING AND DEACREASING INTERVALS

MULTIPLICITY OF ZEROS