Skill 5 Part I Skills 5A Thru 5G Polynomial Functions Test on Thursday 3/3/16

Skill 5 Review #2

Part 1

Skill 5 Part I –Skills 5a thru 5g – Polynomial Functions Test on Thursday 3/3/16

Skill 5 Part II – Skills 5h thru 5j – Rational Functions Test on Tuesday 3/8/16

1.) True or False. is a polynomial function.

2.) True or False. is a polynomial function.

3.) True or False. is a polynomial function.

4.) Determine the leading coefficient: -2

Determine the degree: 5

5.) Determine the leading coefficient:

Determine the degree: 3

6.)
/ 7.)

True or False. / This graph is smooth. / True or False. / This graph is smooth.
True or False. / This graph is continuous. / True or False. / This graph is continuous.
True or False. / The domain of this graph is all real numbers. / True or False. / The domain of this graph is all real numbers.
True or False. / This is the graph of a polynomial function. / True or False. / This is the graph of a polynomial function.
8.)
/ Choose the correct end behavior (circle your answer)
A)
B)
C)
D)
9.)
/ Choose the correct end behavior (circle your answer)
A)
B)
C)
D)
10.)
/ 11.)

True or False. / This graph is smooth. / True or False. / This graph is smooth.
True or False. / This graph is continuous. / True or False. / This graph is continuous.
True or False. / The domain of this graph is all real numbers. / True or False. / The domain of this graph is all real numbers.
True or False. / This is the graph of a polynomial function. / True or False. / This is the graph of a polynomial function.
12.) . Choose the correct end behavior (circle your answer)
A) / B)
C) / D)
13.) . Choose the correct end behavior (circle your answer)
A) / B)
C) / D)

14.)

A) Determine the x-intercept(s).

B) Determine the y-intercept.

Note: polynomial functions have exactly one y-intercept.

15.)

A) Determine the x-intercept(s).

Factors of 12:
Factors of 1:
List of possibleintercepts:
1 / 1 / 3 / -4 / -12
1 / 4 / 0
1 / 4 / 0 / -12
-1 / 1 / 3 / -4 / -12
-1 / -2 / 6
1 / 2 / -6 / -6
2 / 1 / 3 / -4 / -12
2 / 10 / 12
1 / 5 / 6 / 0

/ Alternate solution (factor by grouping)

B) Determine the y-intercept.

y-intercept

16.) Write a polynomial function, , that has zeros at .

Note: you can pick any leading coefficient and any multiplicities.

17.) Write a polynomial function, , for the graph shown below:

/ Using the x-intercepts;

Using the y-intercept;

18.) Show that is a factor of . Use the result to find all of the factorsof .

-5 / 6 / 41 / 48 / -35
-30 / -55 / 35
6 / 11 / -7 / 0

Note: had it asked for the zeros of the function then the final answer would be;

19.) Determine .

-2 / 1 / 7 / -16 / 17 / -12 / -20 / 31
-2 / -10 / 52 / -138 / 300 / -560
1 / 5 / -26 / 69 / -150 / 280 / -529

Alternate solution

20.) List all of the possible rational zeros for the function

Factors of 6:

Factors of 2:

List of possible rational zeros:

Find the zeros of each function below and indicate if the graph crosses or touches the x-axis at each zero

21.)

/ Zeros / Cross or Touch-n-Turn
/ T-n-T
/ Cross
/ Cross
/ Cross
22.)
Note: Factor by grouping will not work here, we must use the rational zero theorem.
Factors of 6:
Factors of 1:
List of possible rational zeros:
1 / 1 / -6 / 11 / -6
1 / -5 / 6
1 / -5 / 6 / 0

/ Zeros / Cross or Touch-n-Turn
/ Cross
/ Cross
/ Cross
23.)

/ Zeros / Cross or Touch-n-Turn
/ T-n-T
/ Cross
/ Cross