Pre-Calculus - Lesson 14
Synlhe: Division
Last time we did long division. Let's review the process for long
division.
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lxZ 6x3 19x"+16x4
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b7xl4 MK
"7x4/yy
lxq
lxkg
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Now, le'l"s learn how To simplify This process when dividing by a linear
ex
Pre-Calculus - Lesson #3
Solvirg Eguufions - Linear Quadratic, Fractional
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"m Solve The following equations and check your solulian. Clear-1y show
all steps. I
A ,\ /gdl
5G+3)=57{Tx]1
3 :5. 739 :9 (-£
27C+7<§AEK~i ( l8 @(3
\ \/
x I .Qic-g 7 c /Z
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Pre-Calculus - Lesson 17
Limits - Day 1
Intro & Limits at infinity
First, let's take a minute to try and understand what a limit is.
#2
Let's try to find 1imf(x) ;where f(x)= 2A7 +_3 .
XHCK. x D
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the function approaches any particular value as the x-val
Pre-Calculus Lesson 5 - Interval Notation / Inequalities
Interval Notation - The new way we will use to describe sets of numbers
- Think back to inequality graphs
Open circle on graph is represented by ) or (
Closed circle on graph is represented by ] or
Pre-Calculus - Lesson 13
InTermediaTe Value Theorem and Long Division
Make a Table of values and ploT The poinTs on The following graph of The
funcTion f(x) = xS 3x" x1 4x1 .
x-value fix) value
-3 x D
-2 v S'
Given ThaT polynomial funcTions are conTinuo
Pre-Calculus - Lesson 7 - (Ch 1.2)
Increasi /decreasin /even/odd/maxima/minima
Definitions
IncreasingFlgyf ij 7Q W\t\£f lfl/q glow Vl m
l'WL 5%th lo m com/c '«4 will
k) 5AM a
5 alaovCYU/Fl AW Q
lmaw/l LN 13 MO%(/{
Decreasing
f(x) = x3 3x
Use the calcu
Pre-Calculus - Lesson 16
Fundamental Theorem of Algebra
If f(x) is a polynomial function of degree_n_, then f(x) has exactly n
zergs in the Complex Number System.
Corollary - Linear Factorization Theorem - a polynomial of degree
n can be expressed as the
Pee-Calculus - Lesson 6 (section 1,1)
Mn inTr'a
Danigmn - 4 Ft [qGM-{F (sgij (Ya Uh"? W
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Range" A OJFV+ V4.(U-< g (Sul-FAj gm 3% A's '
IndependenT variable - hop 1 oudiijl
Dependenf Variable vaPl/. a V? {ARC M
TesTi for Functions
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Pre-Calculus - Lesson 9 - Ch 1.3
Transformations of Functions
For this lesson we will be dealing with 4 basic functions
f(x):x2 fx):x3
We will investigate what happens when we change the functions.
Let's look at the graphs of some quadratic functions
Wr
Pre-Calculus - Lesson 18
Technigues for EvaluaTing LimiTs
The firsT Technique To evaluaTe a limiT is To simply plug in The value To see if
The funcTion has a value aT ThaT x.
linear1) : g Plug in x=3.
5? MC ! Ll M;
New ET'S Try These.
lim 2x5 Plug in
Pre-Calculus - Lesson 8
N we a»? a
( _
LeT's look 01' a graph of The function f x The slope of the line connecting a point on the graph of a function to a
nearby point is called the Difference: Quotient and is defined as above
as a slope
f(x+l7)af(x)
11
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Pre-Calculus Lesson #2
Circles
The following is the general form for a conic section
Ax2+B +Cy2+Dx+Ey+F=O
We will assume that 3:0, and so leave rotational coordinate systems for
a college Algebra classl Rewrite our version of the general form above.
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