Pre-Calc FInal

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How do you point out a function?

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1

How do you point out a function?

When there is one output value for every x-value

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2

How to determine the domain of a function?

set denominator of action equal to zero

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3

2 RULES

  1. anything divided by zero is undefined

  2. negative in a square root

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4

when writing parentheses

the lower number always goes first!

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5

cosine

adjacent/hypotenuse

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6

Sine

opposite/hypotenuse

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7

Tangent

Oppisite/ adjacent

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8

csc

hyp/op

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9

Secant

hyp/adjacent

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10

Cotangent

adjacent/oppisite

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11

Isosceles Triangle

knowt flashcard image
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12

When finding angles on Unit Circle CSC, SEC, COT

csc→1/Y

sec→ 1/x

Cot→ x/y

(x,y)→ are your coordinates!!

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13

a^2+b^2=c^2

c^2 is always your hypotenuse

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14

Remember !!

no square roots on denominator!

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15

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

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16

What do you do for a Quadratic Function

-Add to middle

-Multiply to end

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17

Slope Intercept form

y=mx+b

m=slope

x=variable

b=y-intercept

y=variable

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18

Slope

rise/run

  • y2-y2/x2-x1

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19

Quadrents

numbered counter-clock wise area contained by the x &y axis

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20

x&y plane

plane they form at intersection

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21

Cordinate axis’s

2 fixed coordinate lines that form the cordinate plane

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22

origin

2 lines point of intersection

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23

Quadrents

Counter clock wise

2 1

34

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24

Distance Formula

√[(x₂ - x₁)² + (y₂ - y₁)²].

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25

Mid Point Formula

knowt flashcard image
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26

f (x)

F is a machine creating y out of X

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27

Functions →

can only have One output value for every input value!

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28

When Square root is already present in a function

only one version is necessary

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29

When using square root as a solving technique

both + and -

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30

Bracket [=

included

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31

Parenthesis (=

Excluded

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32

IDENTITY FUNCTION y=-f(x)

x-axis reflection making y-negative

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33

IDENTITY FUNCTION y=f(-x)

y-axis reflection

-making x negative

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34

Notation→ (fog)(x)

F(g(x)

“f of g of x”

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35

if you have 2 x-values

you do the domain for both

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36

Quadratic Function standard form

f(x) = ax2 + bx + c

→ a cannot equal 0

→ b, c can be anything!!

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37

Quadratic Formula for x-intercepts

knowt flashcard image
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38

How to solve for vertex?

x=-b/2a

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39

if in standard form and leading coefficient is postive=

opens up

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40

If leading coefficient is negative and in standard form =

opens down

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41

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

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42

Exponents both (+) or (-)

→ touches (Bounces)

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43

Opposite

crosses x-axis

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44

x-intercepts

where x=o

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45

Multiplicity even→

graph bounces off x-axis

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46

Multiplicity odd→

graph crosses x-axis

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47

huge/tiny=

normal/tiny=

HUGE

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48

normal/huge=

Still really tiny

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49

tiny/tiny

could be tiny, normal or huge

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50

Whats an asymptote?

a line or a curve that a function goes close to and might NEVER touch

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51

Aysmptotes do NOT ..

X-axis

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52

Rational Functions

a function defined as the quotient (division) of two polynomials

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53

Asmpytotes may..

never be touched or be crossed by a function

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54

Asymptotes of Polynomials

standard form

<p>standard form</p>
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55

In order to solve for vertical asymptotes

set denominator equal to zero

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56

How do you get a hole!

cancels out completely

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57

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

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58

Rational functions.

x- intercept →numerator

domain→ denominator

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59

Orignial formula (Continious compounding interest formula)

P(t)=Pe^rt

p=principal

e= e on calculator

r= rate of interest

t=time in years

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60

y=log a ^x

form

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61

Exponential Form

base^exponent= result

a^t=R

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62

Logarithmic form

knowt flashcard image
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63

Degree to radians →

x pie/180

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64

Radioans to Pie→

x 180/pie

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65

For a Rational Function. intruder to find x-intercepts

set numerator equal to zero

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