Polynomial Functions Review

degrees

100

the highest power of a polynomial is called the ____

degree

200

the degree of a polynomial is located with the _______ term

leading

300

Name the DEGREE of the following:

-x³ + 3x² + 1

3

400

Name the degree of the following:

3x³ - x⁵ +2x⁴ - 2

5

500

Name the degree:

(x² + 13)(2x⁵ -4)

7

end behavior

100

Describe the END BEHAVIOR using 2 words:

2x⁴ + 5

Even / Positive

200

Describe the END BEHAVIOR using 2 words:

-3x² +2x - 1

Even/Negative

300

Describe the END BEHAVIOR using 2 words (*hint - check for standard form!)

3x² - x⁵ + 1

negative/odd

400

Describe the END BEHAVIOR using 2 words:

(x² - 8x + 16)(2x+1)

positive/odd

500

Describe the END BEHAVIOR using 2 words:

(-3x³ +9x² - 12)(4x² - 1)(2x)

negative/even

limit notation

100

For a POSITIVE/EVEN function, as x --> infinity, y --> ______ 

(positive) infinity

200

For a POSITIVE/ODD function, as x --> negative infinity, y--> ______

(negative) infinity

300

For a NEGATIVE/EVEN function, as x --> negative infinity, y --> ________

negative infinity

400

For a NEGATIVE/ODD function, as x--> infinity, y--> ________

negative infinity

500

Describe (using LIMIT NOTATION) the end behaviors of the following function:

y = 5x⁴

x--> infinity, y--> infinity

x--> negative infinity, y--> infinity

even functions

100

An EVEN function will be symmetric through the _______________

y-axis

200

An EVEN function passes through the point (4,5).  What other point MUST lie on the graph?

(4,-5)

300

An EVEN function passes through the point (-3,6).  What other point MUST lie on the graph?

(3,6)

400

TRUE or FALSE:

y = 2x² - 5 is an EVEN function?  Tell why or why not!

TRUE / symmetric over the y-axis

500

TRUE or FALSE:

f(x) = 1/5x³ + x² + 2?  Explain why or why not.

FALSE / Not symmetric over the y-axis

odd functions

100

An ODD function will be symmetric through the _______________

origin

200

An ODD function passes through the point (-5,-4).  What other point MUST be on the graph?

(5,4)

300

An ODD function passes through the point (7,3).  What other point MUST be on the graph?

(-7,-3)

400

TRUE or FALSE:

y=x is an ODD function? Explain why or why not.

TRUE.  Symmetry through the origin.

500

Is the following function ODD / EVEN / or NEITHER?

y = 4x³ - x

Tell how you know!

ODD

symmetric through the origin / opposite x's produce opposite y's