Algebra 3: Polynomial Unit
Review
I. A.APR.3 Learning Target: I can sketch a
graph of the polynomial using the zeroes and end
behavior
1. Given the function f ( x)  x3  x 2  10 x  8
Name ______________________________________
Period _______________ Date _________________
2. Given the function f ( x)  x3  6 x 2  x  30 .
Part A: Determine if (x – 2) is a factor. Show all
work.
Part A: Identify all the possible rational roots.
Circle one:
Answer: _________________________
YES
NO
Part B: If so, list all factors. If not, explain why
not.
Part B: Identify the zeroes of the function.
Answer: _________________________
Part C: Describe the end behavior of the function.
__________________________________________
__________________________________________
__________________________________________
Part D: Use this information to sketch the graph of
the function.
Algebra 3: Polynomials Review
6/4/14
Answer: __________________________________
__________________________________________
__________________________________________
_________________________________________
PUHSD Algebra 3-4 Curriculum Team
II. A.REI.11 Learning Target: I can identify the
points of intersection of two or more functions.
5. Explain why a table may not be the best way to
find the points of intersection of two functions.
3. Use a graphing calculator to find the approximate
intersection(s) to the nearest tenth.
_____________________________________________
_____________________________________________
f ( x)  x 2  2 x  8
_____________________________________________
g ( x)  x 3  3 x 2  8
_____________________________________________
III. F.IF.4 Learning Target: I can interpret key
features of graphs and tables in terms of the
quantities, and sketch graphs showing key features
given a verbal description of the relationship
6. Use the graph to Identify the roots and their
multiplicities to fill in the table below
Answer: _________________________
4. Create a table with x, f(x) and g(x) and then
identify the points of intersection of the
functions.
f ( x)  x 4  2 x 2  4
g ( x)  x 5  x 3  4
Even Multiplicity Roots
x
f(x)
Odd Multiplicity Roots
g(x)
-3
-2
-1
0
1
2
3
Answer:__________________________________
_________________________________________
Algebra 3: Polynomials Assessment
6/4/14
PUHSD Algebra 3-4 Curriculum Team
7. The graph of a function is given below.
IV.
F.IF.9 Learning Target: I can compare
properties of two functions each represented
in a different way.
8. Examine the functions below and fill out the
chart using <, >, or = to compare the two and
answer the question.
f ( x)  3x 2  2 x  3
g(x)
Part A: State the intervals in which the function
decreases.
Part A:
__________________________________________
f(x)
Number of real
x-intercepts
x-value of largest
x-intercept
Minimum on the
interval [0, 2]
Rate of change over
[-1, 1]
__________________________________________
Part B: State the intervals in which the function
increases.
__________________________________________
g(x)
Number of real
x-intercepts
x-value of largest
x-intercept
Minimum on the
interval [0, 2]
Rate of change over
[-1, 1]
Part B: How do the end behaviors of
f ( x ) and g ( x ) compare as x approaches infinity?
__________________________________________
__________________________________________
__________________________________________
__________________________________________
Part C: Which equation has a greater maximum?
How do you know?
__________________________________________
__________________________________________
__________________________________________
Algebra 3: Polynomials Assessment
6/4/14
PUHSD Algebra 3-4 Curriculum Team
9. The function y  (2 x  5)3 is transformed to:
Part A: y  (2 x  5)3  8 Describe in words how
the function has been transformed:
__________________________________________
__________________________________________
__________________________________________
Part B: y  (2 x  5)3 Describe in words how the
function has been transformed.
__________________________________________
__________________________________________
__________________________________________
Algebra 3: Polynomials Assessment
6/4/14
PUHSD Algebra 3-4 Curriculum Team