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Flashcards for Units 3 & 4 for the new AP Precalculus

1

**Periodic function**

A function that consistently reproduces a pattern of y-values

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2

Period

The interval period between a periodic function's repeats

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3

Intervals of increase

It is the collection of x-values extending from the greatest point to the lower bound. This is represented as [a,b], where b is the maximum point's x-value in the case of the first period.

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4

Intervals of decrease

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5

Concavity

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6

**Average rate of change**

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7

**Standard position**

If an angle's initial side is parallel to the positive x-axis and its vertex is at the origin, it is said to be in standard position.

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8

**Initial side**

The ray on the

x-axis

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9

**Terminal side**

An angle's other ray in standard position

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10

**Radian**

The measurement of an angle θ that, when represented as a central angle, subtends an arc with a length equal to the circle's radius

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11

**Coterminal angles**

Angles with a common terminal side in standard position

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12

**Reference angle**

An acute angle made up of the x-axis and the angle's terminal side

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13

**Phase shift**

When an angle is added, the sine or cosine function shifts horizontally.

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14

**Frequency**

The reciprocal of a function's period is the number of times the function repeats its values within a specified interval.

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15

**Amplitude**

The half of a periodic function's range between its maximum and minimum values

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16

Midline

A periodic function's horizontal line passing through the average of its maximum and minimum values

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17

**Sinusoidal function**

Whatever function of the form y=asin[b(x−c)] + y=asin[b(x−c)]+d that follows a sine wave pattern

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18

**Parametric function**

A parameter, t, is an independent variable that determines the relationship between two dependent variables, x and y, which are represented by a function. A pair of parametric equations is commonly used to represent parametric functions.

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19

Parameter

In a parametric function, the values of the dependent variables, y and x, are influenced by the independent variable, t.

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20

**Parametric equations**

A pair of formulas characterizing a parametric function, wherein each formula represents one of the dependent variables, x or y, in relation to the independent variable, t.

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21

R²

The area where parametric functions are graphed is commonly represented by the set of all ordered pairs of two real numbers.

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22

**Table of values**

The dependent variables, y i and x i, are evaluated at various values of the independent variable, t i, within the domain of a parametric function, yielding a numerical table.

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23

**Graph of a parametric function**

A graphic depiction of a parametric function, in which the points are connected in ascending order of increasing value of t, and the coordinates (t, t)(x, y, i) are plotted in the plane for a range of values of t.

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24

**Particle motion**

Parametric functions in a two-dimensional plane can be used to simulate a particle's motion in space.

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25

**Horizontal extrema**

The maximum and minimum values of the function x(t) correspond to the furthest points a particle can travel in a horizontal direction.

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26

**Vertical extrema**

The maximum and minimum values of the function y(t) correspond to the furthest points a particle can travel in a vertical direction.

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27

**Direction of motion**

The direction in which a particle travels in the plane; the x and y components can be examined separately.

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28

**Rate of change**

A measurement of the speed at which one variable changes in relation to another.

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29

**Average rate of change**

the proportion of a function's output change to its input change over a specified period of time.

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30

**(cos t,sint)**

An angle formed by the positive x-axis and a line segment from the origin to the point is represented by the parameter t in this parametric representation of a point on the unit circle.

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31

**Transformations**

A figure's size, position, or direction within a mathematical space can all be changed with these operations. It is possible to alter the path that parametric equations represent by utilizing transformations.

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32

**Scaling**

This kind of transformation modifies a figure's size without changing its shape. A circle's radius changes when it is scaled.

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33

**Translating**

This kind of transformation shifts a figure's points all in the same direction and by the same amount. A circle's center is moved to a new location on the coordinate plane when it is translated.

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34

**Reflecting**

This kind of transformation causes a figure to be flipped over a plane (in 3D) or a line (in 2D). Motion is changed from counterclockwise to clockwise, or vice versa, by reflecting a circular path.

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35

**Implicitly defined function**

A function in which an equation involving the two variables is used to express the dependent variable rather than using the independent variable alone.

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36

**Explicit function**

A function where the independent variable and the dependent variable are clearly expressed.

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37

**Positive ratio**

Both variables either simultaneously increase or decrease when the ratio of the changes in the two variables is positive.

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38

Negative Ratio

When the two variables' change ratio is negative, one variable rises while the other falls.

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39

**Matrix**

A numerical or variable array arranged rectangle-wise

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40

**Square matrix**

A matrix with order m x m

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41

**Row matrix**

A matrix arranged in a 1 by m. Example: 1×3 matrix

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42

**Column matrix**

A matrix arranged in a m by 1. Example: 3×1 matrix

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