use your calculator to graph the following equation in the same window:
a)
y=x'
b)
y:1*'
4
I
c) y=-x2
.-3)
d) y=-x2
Show your graphs here. Draw the graphs accurately, being especially careful to get the right values at
1 andx: -1.
a)
b)
c)
d)
Whatisthedif
lf-UVnomial
-r,"
Functions
u"r *.\-t,*"* c* rur#.r.*,. Algebfa ll NOteS
Polynomial in one variable: A polynomial degree n in one variable x is an expression where the numbers in front
of the variables are integers. Ex) 3xa + 4x3 - 6xz + 4x - 7
The degree
Date';., JJ
Period ffi
7-7 Operations of Functions
Algebra of Functions: Finding the sum, difference, product, and quotient of functions to
new functions.
Algebra of
Sum
Functions
Difference
Lf +sxx) = f (x)+ g(x)
U-s)@)=f(x)-g(x)
Product
(f.s)@)=f(x).g(x
Period
Date
7-8 Inverse Functions
& Relations
Inverse Relations
Two relations are inverse relations if and only if whenever on relation contains
the element (a,b)" the other relation contains the element (b,a)
Property of
Inverse Functions
Suppose
f
andf-
Name
7-9
S
uare Root Functions and In
ualities
A function that contains the square root of a variable expression.
Transformations
Like parabolas (quadratic functions), square root functions can be graphed
using transformations.
+ k , where a:vertical stre
7
*or.
T&Fvop
[.r",a*,u
oor. r f raf oq *
n,
PERIoD
t'
(continued)
Chapter 6 Review
12. The quadratic equation xz + &: 1 is to be solved by completing the square'
Which equation would be the first step in tlat solution?
B-x2+6n+36:1+36
A.x2+fu-1:o
u.&
D'-
Name
SnrrGh fite'rande,
Date
\ec
period
\u
6.3 Factoring Review
Example) Factor 4-term polynomials by grouping.
a) 12mn+36m-2n-6
1. Factor out GCF
(if any).
GCF:
A (Gvmnrttrn-"j)
J
GCF
C
2. Group into two groups.
( kv!"rn
GCF
^
ct (
3. Find GCF of each gr
F
Name
Sava\n (lO. . avdsur
oate
\et-
Period 1
\t(
6.4 Completing the Square
Square Root
Property I Fo, ury real number x, ifx2 = n , thenx = +Ji
.
Example) Solve each equation by using the square root property.
a) x2 -8x+16=25
1. Rewrite polynomial in pe
5-6 Radical Expressions
Objective 1: Use the product rule for radicals.
Product Rule for Radicals: lf qfa and tl6 are rea] numbers, then cfw_a . lt6
To simplify a square root, follow these steps:
1. Factor the radicand into as many squares as possible.
2.
5-7 Rational Exponents
Objective 1: Understand the meaning ol a* .
Definition: lf r is a positive integer greater than 1 and da is a real number, lhen da : a*
*Notice that
the denominator of the rational exponent corresponds to the index of the radical.
E
5-8 Radical Equations
Objective 1: Solve equations that contain radical expressions.
Solving a Radical Expression
Step 1: isolate one radical on one side of the equation.
Step 2: Raise each side of the equation to a power that will eliminate the radical a
5-9 Complex Numbers
Objective 1: Define imaginary and complex numbers.
lmaginary unit: i L 1:7
i2 =4
. Ja i,la
exl ,[4
];1
a
:
:
Example 1: Write with i notation.
a)'IFIA
c)
l-1
-'dw
A.
UJ
L!
r'"
,a-
4',+*.'
Example 2: Multiply or divide as indicated.
a)
Scr.o.'-v. CLt'.- <2e,.r ."gt",t Y
Graphing Quadratic Functions
I.
The parent function
!
= x2
Use a table to plot points and graph:
x
(x,
!=x2
o
0
t/2
-t/2
L/)
'/:
,'1ur\
'ir . 'jrl\
,LI
\
2
n
y)
\o,
tl.r
-l
! = x2. Show your work here:
t 1r li
Ll
q
q
-1