Review and Supplemental Review Unit 2b: Polynomial and Rational Functions

Review and Supplemental Review
2.1: Quadratics, Parabolas, Standard
Form
Unit 2b: Polynomial and Rational Functions
1.
The graph of
is shifted 1 units to the right and 1
units down. What is the equation of
the new graph written in standard
form?
2.
Write
in standard
form. Identify the vertex, axis of
symmetry, and zeros.
In terms of SRT transformations, how
does the graph of the function in Q2
differ from its parent function?
4.
Write a quadratic function whose
graph passes through (−2, −8) and
whose vertex is at (−4, −6).
5.
Identify the vertex of
2.2: Polynomial Functions, End Behavior,
Multiplicity
7.
Describe the degree and leading
coefficient of the polynomial function
graphed below.
8.
Bookwork:
P. 208: 19
3.
6.
Write a function whose graph has the
following end behavior:
As
,
As
,
.
Without graphing the function,
describe the end behavior of
As
As
y
x
9.
The graph of a polynomial function of
degree 5 is tangent to the -axis at
(0, 0) and crosses the -axis at (−4, 0).
If those are the only zeros of the
function, and the graph passes
through the point (−2, 6), what is the
equation of the function?
10. Let
a) How many zeros does
.
have?
b) How many distinct zeros does
c)
have?
Describe the behavior of the graph at
.
d) Describe the behavior of the graph at
.
e)
.
Describe the behavior of the graph at
,
,
_____
_____
2.3: Polynomial Division
11. Use synthetic division to divide
[
] into
12. What conclusion can you draw about
Q11 based on the remainder?
13. Find the value of k such that the
divides evenly into
.
2.4: Complex Numbers
14. Write in standard form:
15. Perform the operation and write in
standard form:
16. Find the value of :
17. Expand
2.5: Zeros of Polynomials
Bookwork:
P. 209: 49
P. 209: 54
18. Write a polynomial function
of
least degree that has rational
coefficients, a leading coefficient of 1,
and has 2,
, and
as zeros.
19. Explain why a polynomial of odd
degree must have at least one
rational zero.
21. Use the table below to help you find the zeros of the function. Then graph the
function.
-3
-2
-1
0
1
2
3
-50
21
12
-5
42
225
616
Bookwork:
P. 210: 83-88 (86, 88)
P. 210: 89
P. 210: 91-96 (92, 96)
P. 210: 99-102 (100)
P. 210: 103-106 (104, 106)
P. 210: 108
20. Let
be a polynomial such that
and
. Explain
why
must have a zero between
and
.
22. Find all the zeros of the function and then graph it.
2.6: Rational Functions
23.
Bookwork:
P. 210: 113, 114
For Q23-Q29, sketch the graph of each
rational function without the aid of a
graphing utility. But first a) find the
vertical asymptotes, b) find the
horizontal/slant asymptote, c) find the and -intercepts, and then finally d)
graph the thing.
24.
26.
25.
27.
28.
29.
30.
4
the dashed graph. Graph ( )
2
5
2
4
is the solid graph and
is
.