Units 3 & 4 AP Precalculus Flashcards

Flashcards for Units 3 & 4 for the new AP Precalculus

Periodic function

Periodic function

A function that consistently reproduces a pattern of y-values

Period

The interval period between a periodic function's repeats

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.

Intervals of decrease

Concavity

Average rate of change

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.

Initial side

The ray on the

x-axis

Terminal side

An angle's other ray in standard position

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

Coterminal angles

Angles with a common terminal side in standard position

Reference angle

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

Phase shift

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

Frequency

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

Amplitude

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

Midline

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

Sinusoidal function

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

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.

Parameter

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

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.

R²

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

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.

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.

Particle motion

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

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.

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.

Direction of motion

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

Rate of change

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

Average rate of change

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

(cost,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.

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.

Scaling

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

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.

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.

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.

Explicit function

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

Positive ratio

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

Negative Ratio

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

Matrix

A numerical or variable array arranged rectangle-wise

Square matrix

A matrix with order m x m

Row matrix

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

Column matrix

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