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Pre-Calc FInal
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65 Terms
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1
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How do you point out a function?
When there is one output value for every x-value
2
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How to determine the domain of a function?
set denominator of action equal to zero
3
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2 RULES
1. anything divided by zero is undefined
2. negative in a square root
4
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when writing parentheses
the lower number always goes first!
5
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cosine
adjacent/hypotenuse
6
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Sine
opposite/hypotenuse
7
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Tangent
Oppisite/ adjacent
8
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csc
hyp/op
9
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Secant
hyp/adjacent
10
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Cotangent
adjacent/oppisite
11
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Isosceles Triangle
12
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When finding angles on Unit Circle CSC, SEC, COT
csc→1/Y
sec→ 1/x
Cot→ x/y
(x,y)→ are your coordinates!!
13
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a^2+b^2=c^2
c^2 is always your hypotenuse
14
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Remember !!
no square roots on denominator!
15
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Compound Interest Formula!
A=P(1+r/n)^rn
\
\
P=Principe balence
r= interest rate
n= number of times interest applied per time period
t= number of time periods elapsed
\
16
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What do you do for a Quadratic Function
\-Add to middle
\-Multiply to end
17
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Slope Intercept form
y=mx+b
m=slope
x=variable
b=y-intercept
y=variable
18
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Slope
rise/run
* y2-y2/x2-x1
19
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Quadrents
numbered counter-clock wise area contained by the x &y axis
20
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x&y plane
plane they form at intersection
21
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Cordinate axis’s
2 fixed coordinate lines that form the cordinate plane
\
22
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origin
2 lines point of intersection
23
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Quadrents
Counter clock wise
\
2 1
34
24
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Distance Formula
√\[(x₂ - x₁)² + (y₂ - y₁)²\].
25
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Mid Point Formula
26
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f (x)
F is a machine creating y out of X
27
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Functions →
can only have One output value for every input value!
28
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When Square root is already present in a function
only one version is necessary
29
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When using square root as a solving technique
both + and -
30
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Bracket \[=
included
31
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Parenthesis (=
Excluded
32
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IDENTITY FUNCTION y=-f(x)
x-axis reflection making y-negative
33
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IDENTITY FUNCTION y=f(-x)
y-axis reflection
\-making x negative
34
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Notation→ (fog)(x)
F(g(x)
\
“f of g of x”
35
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if you have 2 x-values
you do the domain for both
36
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Quadratic Function standard form
f(x) = ax2 + bx + c
→ a cannot equal 0
→ b, c can be anything!!
37
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Quadratic Formula for x-intercepts
38
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How to solve for vertex?
x=-b/2a
39
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if in standard form and leading coefficient is postive=
opens up
\
40
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If leading coefficient is negative and in standard form =
opens down
41
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Steps in solving a Quadratic Equation
1. Opens up/down
2. X-intercepts set equation = to zero
3. Y-intercept , set x=0
4. Factoring
42
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Exponents both (+) or (-)
→ touches (Bounces)
43
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Opposite
crosses x-axis
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x-intercepts
where x=o
45
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Multiplicity even→
graph bounces off x-axis
46
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Multiplicity odd→
graph crosses x-axis
47
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huge/tiny=
normal/tiny=
HUGE
48
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normal/huge=
Still really tiny
49
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tiny/tiny
could be tiny, normal or huge
50
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Whats an asymptote?
a line or a curve that a function goes close to and might NEVER touch
51
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Aysmptotes do NOT ..
X-axis
52
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Rational Functions
a function defined as the quotient (division) of two polynomials
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Asmpytotes may..
never be touched or be crossed by a function
54
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Asymptotes of Polynomials
standard form
55
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In order to solve for vertical asymptotes
set denominator equal to zero
56
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How do you get a hole!
cancels out completely
57
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How to find horizontal asymptotes
1. if top is heavy there is no horizontal asymptote
2. If the exponents are the same then divide both number
3. If bottom is heavy then it is zero
58
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Rational functions.
x- intercept →numerator
domain→ denominator
59
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Orignial formula (Continious compounding interest formula)
P(t)=Pe^rt
p=principal
e= e on calculator
r= rate of interest
t=time in years
60
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y=log a ^x
form
61
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Exponential Form
base^exponent= result
\
a^t=R
62
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Logarithmic form
63
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Degree to radians →
x pie/180
64
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Radioans to Pie→
x 180/pie
65
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For a Rational Function. intruder to find x-intercepts
set numerator equal to zero
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