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Temple Precalculus > Temple Precalculus Final All > Flashcards

Temple Precalculus Final All Flashcards

1
Q

Definition of a Function

A
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2
Q

2.1 Evaluating a Function Defined

A
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3
Q

Four Ways to Represent a Function

A
  1. Verbal
  2. Visual
  3. Algebraic
  4. Numerical
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4
Q

Function Machine Illustration

A
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5
Q

Piecewise Function defined

A
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6
Q

The Domain of a Function

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7
Q

What about the domain of Radicals

A

Note if the radical is odd or even and the Bracket or parenthesis

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8
Q

Absolute Value and Greatest Integer Function Graphs

A
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9
Q

2.2 Equations that Define Functions

A
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10
Q

2.2 graph of a piecewise defined function

A
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11
Q

Graph of the Greatest Integer Function

A
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12
Q

Linear Function Graph

A
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13
Q

Reciprical Function Graphs

A
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14
Q

Root Function Graphs

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15
Q

The Graph of a Function

A
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16
Q

The Vertical Line Test for Functions

A
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17
Q

Definition of Increasing and Decreasing Functions

A
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18
Q

Getting the Domain and range from a Graph

A
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19
Q

Increasing and Decreasing Functions

A
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20
Q

Local Maxima and Minima of a Function

A
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21
Q

Power Function Graphs Exponents x^n

A
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22
Q

Solving equations and Inequalities Graphically

A
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23
Q

2.6 Even and Odd Function Defined

A
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24
Q

2.6 Even and Odd Functions

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25
Q

General Order of Operations

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26
Q

Horizontal stretching and Shrinking Graphs

A
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27
Q

Order of Operations when Evaluating Functions

A
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28
Q

2.6 Reflecting Graphs

A
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29
Q

Algebra of Functions

A
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30
Q

Composition of 3 Functions

A
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31
Q

Composition of Functions

A
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32
Q

Composition of Functions Defined

A
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33
Q

Definition of the Inverse f a Function

A
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34
Q

Dont Mistake the -1 in f^-1 for an exponent

A
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35
Q

Finding the Inverse of a Function

A
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36
Q

Graphing the Inverse of a Function

A
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37
Q

Horizontal Line Test

A
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38
Q

Inverse Property Function

A
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39
Q

One to One

A
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40
Q

The Inverse of a Function

A
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41
Q

Arrow Notation

A
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42
Q

Definition of Vertical and Horizontal Asymptotes

A
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43
Q

Difference of Squares is

A
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44
Q

Finding Horizontal Asymptotes

A
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45
Q

Finding the Intercepts and Assymptotes and graphing them

A
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46
Q

Finding the Veritcal and Horizontal Asymptotes

A
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47
Q

Finding the x intercept

A
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48
Q

Finding the y intercept

A
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49
Q

Findingthe Vertical Asymptotes

A
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50
Q

Graph of f(x)=1/x

A
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51
Q

Horizontal Asymptote with Translations

A
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52
Q

Transformation of a Rational Function y=1/x

A
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53
Q

Transformations of the Graph of a Rational Function Stretching and Shifting

A
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54
Q

Making a Table to find the Intervals

A
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55
Q

Solving a Polynomial Inequality

A
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56
Q

Solving a Rational Inequality

A
57
Q

Solving Polynomial Inequalities

A
58
Q

Solving Rational Inequalities

A
59
Q

Compounded Interest Formula

A
60
Q

The Natural Exponential Function e

A
61
Q

Graphing the Exponential Functions e^x and e^-x

A
62
Q

Natural Exponent e^x graph transformations

A
63
Q

Continuously Compounded Interest

A
64
Q

The Number e

A
65
Q

Common Logarithms

A
66
Q

4.3 Definition of Logarithmic Functions

video

http://college.cengage.com/mathematics/blackboard/shared/content/video_explanations/video_wrapper.html?filename=kazmierczak/srwp60403a&title=Logarithmic%20Functions%20I

A
67
Q

Definition of the Logarithmic Function

A
68
Q

Graph of the Family of Logarithmic Functions

A
69
Q

Graph of the Logarithmic Function

A
70
Q

Graph of the Natural Logarithmic Function

A
71
Q

Graphing a Logarithmic Function by Plotting Points

A
72
Q

Inverse Function Property Domain

A
73
Q

Inverse Property Function

A
74
Q

Log to Exponential Form

A
75
Q

Natural Logarithms

A
76
Q

Omitting the Parenthesis

A
77
Q

Properties of Logarithms

A
78
Q

Properties of Natural Logarithms

ln

A
79
Q

The Natural Logarithmic function is the inverse of the natural exponential function

A
80
Q

Expanding and Combining Logarithmic Expressions

PG 355

A
81
Q

Since Logarithms arw exponents the Laws of Exponents give Rise to the Laws of Logarithms

http://college.cengage.com/mathematics/blackboard/shared/content/video_explanations/video_wrapper.html?filename=kazmierczak/srwp60404&title=Laws%20of%20Logarithms

A
82
Q

WARNING There is no corresponding Logarithm Rule for of a Sum or a Difference

pg 356

A
83
Q

http://college.cengage.com/mathematics/blackboard/shared/content/video_explanations/video_wrapper.html?filename=kazmierczak/srwp70405&title=Compound%Interest

A
84
Q
  1. 5 Exponential Equation Inequality
    https: //www.webassign.net/v4cgi/extra/bc_enhanced/index.tpl?asset=watch_it_player&asset_url=/bc_enhanced/sprecalc7_w_player/scolalg5_05_04_070.html&UserPass=40416dd1f85ab2d92f82bfef24bd5be5
A
85
Q

http://college.cengage.com/mathematics/blackboard/shared/content/video_explanations/video_wrapper.html?filename=kazmierczak/srwp60405&title=Exponential%20Equations

A
86
Q

4.5 Guidlines for Solving Exponential Equations

A
87
Q

4.5 Solve the Logarithmic Equation for x

A
88
Q

Solving an Exponential Equation by isolating the exponential term

A
89
Q

Solving an Exponential Equation by isolating the exponential term

A
90
Q

Using the Quadratic Equation to Solve a Logarithmic Equation

A
91
Q

When an exponential equation is a quadratic equation

It must be factored

A
92
Q

When the Exponential Equation has A Common Factor

A
93
Q

When x is in the denominator of an exponential equation

A
94
Q

When x is on both sides of the exponent

A
95
Q

When x is on both sides of the exponent

A
96
Q

4.6 Need Exponential Growth

A
97
Q

get it from book problems pdf

A
98
Q

Finding the Period of Sine and Cosine Curves

period=2π/k

A
99
Q

Graph of the unit circle values

http://college.cengage.com/mathematics/precalculus/animations/stewart/sp060503f02.html

A

Note the color pattern as the circle stretches along the line as one period of 2π

100
Q

Horizontal Shift on a Graph

Remember it is the part (x-b)

and is a shift in an Unexpected Direction

this affects x so it is in the parenthesis with x

A
101
Q

One period of x=cosine t

0≤ t ≤2π

A

Graph of cos t for

0≤ t ≤ 2π

102
Q

One period of y=sin t

0≤ t ≤2π

A

Graph of sin t for

0≤ t ≤2π

103
Q

https://www.webassign.net/v4cgi/extra/bc_enhanced/index.tpl?asset=watch_it_player&asset_url=/bc_enhanced/sprecalc7_w_player/sprecalc6_05_03_043.html&UserPass=44b63ef21500978162e459f571f147ab

A

From the graph the period =2π

so

2π/k=2π

k=1

104
Q

Periodic Properties of Sine and Cosine

Sine of t

or Cosine of t

remain the same as you ad 2π periods

A
105
Q

Reflection of a Cosine Curve

A

Reflction of a cosine curve -cos

106
Q

Vertical Stretching and Shrinking of a Sin Graph

AMPLITUDE is the true Value of the number in front of the sin or cos

⎢a⎥sin

A

The Higher the number the higher the peaks

y=2 sin x

Fractions cause Flatter Graphs

y=1/2 sin x

107
Q

Vertical transformaton of Cosine Curve

A

Vertical transformaton of Cosine Curve by +2

108
Q

The Cotangent graph does not cross the origin and swigs to the left

A
109
Q

Periodic Properties of

tan

cot

sec

csc

A
110
Q

The secant and cosecant period is 2π/k

A
111
Q

Tangent and Cotangent figuring the period

π/k

A
112
Q

Tangent Graph crosses the origin and swings to the right

A
113
Q

The Cosecant Graph looks like a U between 0 and π in the first quadrant

with a period of π

and is an upside down U in quadrant 2

A
114
Q

The secant graph has a period of 2π and looks like a U straddling the y axis

A
115
Q

Inverse Cosine Function

A
116
Q

Inverse Sine Function

A
117
Q

Inverse Tangent Function

A
118
Q

Angles in standard position all start (initial side) on the positive x axis

A
119
Q
  1. 1 Converting between Radians and Degrees
    https: //www.webassign.net/v4cgi/extra/bc_enhanced/index.tpl?asset=watch_it_player&asset_url=/bc_enhanced/sprecalc7_w_player/sprecalc6_06_01_005.html&UserPass=bd5ee596620b98562a811b6665bca489

and

https://www.webassign.net/v4cgi/extra/bc_enhanced/index.tpl?asset=watch_it_player&asset_url=/bc_enhanced/sprecalc7_w_player/sprecalc6_06_01_017.html&UserPass=bd5ee596620b98562a811b6665bca489

A
120
Q

Coterminal Angles-have the same initial and terminal sides just have more rotations of 360° or 2π

https://www.webassign.net/v4cgi/extra/bc_enhanced/index.tpl?asset=watch_it_player&asset_url=/bc_enhanced/sprecalc7_w_player/sprecalc6_06_01_035.html&UserPass=bd5ee596620b98562a811b6665bca489

A

Positive Coterminal Angles add multiples of 360° or 2π

Negative Coterminal Angles subtract multiples of 360° or 2π

121
Q

Positive and Negative Angles are determined by the movement of the terminal side away from the initial side

clockwise-negative

counter clockwise-positive

A
122
Q

How Radians (the preferred angle measure in calculus) are measured

A

Note the arc created by the line is the same length as the line or 1 radian

123
Q

Trigonometry of right Triangles-

The Special Two Triangles to Remember

http://college.cengage.com/mathematics/blackboard/shared/content/video_explanations/video_wrapper.html?filename=kazmierczak/srwp70602&title=Trigonometric%20Ratios%20and%20Special%20

A
124
Q

Height of a Building

Angle of Elevation

Angle of Depression

Line of Sight

A
125
Q

Height of a Tree

A
126
Q

Interactive Unit Circle

A

https://www.mathsisfun.com/algebra/trig-interactive-unit-circle.html

127
Q

The Reciprocal Relations in Trig

Cosecant

Secant

Cotangent

A
128
Q

SOHCAHTOA

A
129
Q

The Unit Circle Cosine,Sine

A
130
Q

The Trigonomic Ratios to Remember

A
131
Q

Definition of Trigonomic Functions

A
132
Q

Fundemental Identities of Trig

A
133
Q

Reference Angle

A
134
Q

All Students Take Calculus

A

All Students Take Calculus

135
Q

Reciprical identities

Pythagorean Identities

Even Odd Identities

Cofunction Identities

A
136
Q

Addition and Subtraction Formulas

A
137
Q

Double Angle Formulas

A
138
Q
A

Temple Precalculus (3 decks)

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