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1

Function Notation

A way to name and evaluate functions

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2

Difference Quotient

F(x+h)-f(x)

—————, h=0

h

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3

Point Slope form

Y-y1=m(x-x1)

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4

Slope Intercept form

Y=mx+b

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Slope

Rate of change

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“b” in y=mx+b

Y intercept

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Slope of a horizontal line

Slope=0

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Standard form

Ax+by=C

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Input variables

Domain

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X-coordinate of the point where a line crosses the horizontal axis

X-intercept

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Slopes of perpendicular lines

Slopes are negative reciprocals

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Point where two lines intersect

Solution to a system of equations

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Reciprocal

Multiplicative inverse

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Slope of a vertical line

The slope is undefined

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Output variables

Range

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General form

Ax+By+C=0

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17

Piecewise function

A function defined b two r more equations over a specified domain

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18

Vertical line test

Way to tell if a graph is a function visually

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19

Equation to find slope

M=(y2-y1)/(x2-x1)

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20

Domain explanation

Domain is the furthest x value to the left and right

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21

Range explanation

Highest and lowest y values

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22

Polynomial function the 0 degree is what kind of function

Constant function

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23

Polynomial function the 1st degree is what kind of function

Linear function

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24

Polynomial function the 3rd degree is what kind of function

Cubic function

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25

what does “n” represent in the leading coefficient test

The degree of the function

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How does the graph behave when “n” is odd and the leading coefficient is positive

Falls to the left and rises to the right

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How does the graph behave when “n” is even and leading coefficient is positive

Rises to the left and rises to the right

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How does the graph behave when “n” is odd and leading coefficient is negative

Rises to the left and falls to the right

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How does the graph behave when “n” is even and leading coefficient is negative

Falls to the left and falls to the right

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Asymptotes

Lines that a graph of a function approaches but never touches

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N(x) represents

The numerator

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D(x) represents

The denominator

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Asymptotes effect the graphs

End behavior

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If the degree of the numerator N(x) is less than the degree of the denominator D(x) the graph has a horizontal asymptote at

Y=0

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If the degree of the numerator N(x) is equal to the degree of the denominator D(x) the graph of “f” has a horizontal asymptote at where “a” and “b” are the leading coefficients of N(x) and D(x) respectively

Y=a/b

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If the degree of the numerator N(x) is greater than the degree of the denominator D(x) the graph of “f” has

No horizontal asymptote

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Multiplicity

When one answer is worth three for example X^3=0 is x=0 three times

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The imaginary unit

“i”

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quadratic formula

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Vertex form of parabolas

Y=a(x-h)^2+k

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what does “h” in vertex form represent

X coordinate of the vertex

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What does the “k” in vertex form represent

Y coordinate of the vertex

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formula to find the vertex of a parabola

X= -b/2a

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Axis of symmetry on a parabola

The point that divides the graph into two halves

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Formula used when compounding a certain amount of time (ex. A year)

A=P(1+r/n)^nt

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“N” value when compounded annually

1

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“N” value when compounded semiannually

2

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“N” value when compounded quarterly

4

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“N” value when compounded bimonthly

6

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“N” value when compounded monthly

12

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“N” value when compounded semimonthly

24

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“N” value when compounded bi weekly

26

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“N” value when compounded weekly

52

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“N” value when compounded daily

365

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“N” value when compounded continuously

E

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Amplitude

vertical stretch/ compression (height of one wave)

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Period

Horizontal stretch/ compression (length of one full cycle of the wave)

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Phase Shift

Horizontal shift (determine how far the graph shifts)

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Vertical shift

Shifts the graph up and down

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2pi/b is h used to find what in a sine graph

The period

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When the sine is equal to zero, the close cosecant is ___ and there will be a ____ on the graph

Undefined, asymptote

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When the cosine is equal to __the ____ is undefined and there will be an asymptote

Zero, secant

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Amplitude in a sine and cosine graph

“A” (first value)

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Amplitude in secant, cosecant, and tangent

No amplitude

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Formula used to find the period in a tangent graph

Pi/b

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Angle

Two rays with the same initial point

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Angles that measure between 0 and pi/2 (90) are

Acute

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Shared initial point of two rays

Vertex of the angle

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Angles that measure between pi/2 (90) and pi (180) are

Obtuse

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70

Two positive angles are said to be _______ if the sum of their angles is pi/2 (90)

Complimentary

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Two positive angles are said to be _________ if the sum of their measures is pi (180)

Supplementary

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72

The ____________ is the amount of rotation required to rotate to one side called the ______ to the other side called the _______

Measure of the angle, initial, terminal side

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Two angles in standard position that have the same terminal side are said to be _____

Coterminal

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74

To convert degrees to radians multiple degrees by

Piradians/180

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To convert radians to degrees multiply radians by

180/piradians

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One radian is

The measure of a central angle feta that intercepts an arc *s* equal in length to the radius *r* of the circle

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The radian measure of any central angle is

The length of the intercepted arc divided by the circle’s radius

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How to find a co-terminal angle

Add or subtract 360 degrees of 2pi

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Standard position

1.) It’s vertex is at the origin of a rectangular coordinate system

2.) It’s initial side lies along the positive x-axis

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Sine=

Y and opposite/hypotenuse

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Cosine=

X and adjacent/hypotenuse

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Tangent=

Y/x and opposite/adjacent

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cosecant=

1/y, hypotenuse/adjacent, 1/sin

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Secant=

1/x, hypotenuse/adjacent, 1/cos

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cotangent

X/y, adjacent/opposite, 1/tan

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86

On the Unit circle for every 30 degrees you go ___ radians

Pi/6

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On the Unit circle for every 45 degrees you go every ____ radians

Pi/4

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Y=sin^-1x

[-pi/2, pi/2] (Q1 and Q4)

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Y=cos^-1x

[O, pi] (Q1 and Q2)

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90

Y= tan^-1x

(-pi/2, pi/2) (Q1 and Q4)

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Pythagorean Theorem

A^2+B^2=c^2

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Angle of elevation

An angle formed by a horizontal line and the line of sight to an object that is above the horizontal line (Ex. Looking up at a kite)

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Angle of depression

The angle formed by a horizontal line and the line of sight to an object that is below the horizontal line (Ex. Lookin down from a building)

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Trigonometric Identity

An equation that is true for all values except those for which the expressions on either side of the equal sign are undefined

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component form

PQ

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Magnitude of PQ

IIPQII= √(x2-x1)^2+(y2-y1)^2

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Law of Sines

SinB/b=SinA/a

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When do you use law of sines

ASA AAS

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Law of consines

a^2=b^2+c^2-2(b)(c)(cosA)

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When do you use law of cosines

SAS SSS

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