GRAPHING POLYNOMIALS REVIEW

GRAPHING POLYNOMIALS REVIEW

DOMAIN AND RANGE OF ODD DEFREE POLYNOMIALS

• Polynomials are ODD degree if their arrows are pointing in different direction.

• The polynomial at the right is ODD. Notice that one arrow is going down and the other is going up.

Multiple Select

Which of the following polynomials is / are ODD? Check all that applies.

ODD DEGREE POLYNOMIALS

•  $DOMAIN\ \left(-\infty,\ \infty\right)$  

•  $RANGE\ \left(-\infty,\ \infty\right)$  

Multiple Choice

What is the Domain and Range of the polynomial function?

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

•  $Domain\ \left(-\infty,\ \infty\right)$  

•  $Domain\ \left(\infty,\ -\infty\right)$  

•  $Domain\left(1,\ \infty\right)$  

•  $\ Domain\left(-\infty,\ 1\right)$  

Multiple Choice

What is the range of the function?

 $f\left(x\right)\ =\ x^3-2x\ -1$  

•  $Range\ \left(\infty,\ \infty\right)$  

•  $Range\ \left(-\infty,\ -\infty\right)$  

•  $Range\ \left(-\infty,\ \infty\right)$  

•  $Range\ \left(0,\ -\infty\right)$  

EVEN DEGREE POLYNOMIALS

• EVEN DEGREE polynomials have both arrows pointing in the same direction.

• See example at the right. The polynomial is even as both arrows are pointing into the same direction.

Multiple Select

Which of the following graphs are graphs of EVEN degree polynomials. Check all that applies.

DOMAIN AND RANGE OF EVEN DEGREE POLYNOMIALS

• DOMAIN will always be

   $\left(-\infty,\ \infty\right)$  

• Range will be:

• if opening up   $\left(lowest\ y\ value,\ \infty\right)$  

• if opening down  $\left(-\infty,\ highest\ y\ value\right)$  

• Look at example at the right. The domain is  $\left(-\infty,\ \infty\right)$  while our range is  $lowest\ y\ value\ to\ \inf inity.\left(0,\ \infty\right)\$  

Multiple Choice

What is the domain of the function?

• $\left(-\infty,\ \infty\right)$

• $\left(\infty,\ -\infty\right)$

• $\left(-\infty,\ 1.5\right)$

• $\left(-\infty,\ 1.688\right)$

Multiple Choice

What is the range of the function?

• $\left(-\infty,\ \infty\right)$

• $\left(\infty,\ -\infty\right)$

• $\left(-\infty,\ 1.5\right)$

• $\left(-\infty,\ 1.688\right)$

INCREASING AND DECREASING INTERVALS

• We will be using the x values in determining the increasing and decreasing intervals.

• Always read the graph from left to right.

• Increasing intervals: $\left(-\infty,\ -0.577\right)\ \cup\left(0.577,\ \infty\right)$  

• Decreasing interval:  $\left(-0.577,\ 0.577\right)$  
  
  

Multiple Choice

What is the correct increasing interval?

• $\left(-1.185,\ 0\right)$

• $\left(-1.333,\ 0\right)$

• $\left(-1.185,\ \infty\right)$

• $\left(-1.333,\ \infty\right)$

Multiple Choice

What is the correct decreasing interval?

•  $\left(-\infty,\ -1.333\right)\ \cup\left(0,\ \infty\right)$ 

•  $\left(-1.333,\ \infty\right)\cup\left(0,\ \infty\right)$ 

•  $\left(-1.185,\ \infty\right)\ \cup\left(-\infty,\ 0\right)$ 

• $\left(-1.333,\ \infty\right)$

FINDING ZEROS FROM GRAPHS

• Remember CROSS (1 zero), BOUNCE (2 zeros) and WIGGLE (3 ZEROS)

• The graph bounces at x = 0, Crosses at x= 1 and wiggles at x = 3

• The zeros therefore are : 0, 0, 1, 3, 3 and 3

Multiple Choice

What are the zeros of the graphed polynomial function?

• 0 and 3

• 0, 0 and 3

• 0, 0, 3 and 3

• 0, 0, 3, 3 and 3

Multiple Choice

What are the zeros of the graphed polynomial?

• -1, 0 and 2

• -1, 0, 0 and 2

• -1, 0, 0, 0 and 2

• -1 and 2

Building the function from graph.

• Follow the steps in building the function from graph.

Multiple Choice

What is the correct value of the lead coefficient?

• 1

• -2

• 1/2

• -1/2

Multiple Choice

What is the correct leading coefficient?

• 1

• -2

• 2

• -2

Multiple Choice

What is the correct function graphed?

• $f\left(x\right)\ =\ 3\left(x-1\right)^2\left(x-3\right)$

• $f\left(x\right)\ =\ 3\left(x-1\right)\left(x-3\right)$

• $f\left(x\right)\ =\left(x-1\right)^2\left(x-3\right)$

• $f\left(x\right)\ =\ 2\left(x-1\right)^2\left(x-3\right)$