Units 3 & 4 AP Precalculus Flashcards

A function that consistently reproduces a pattern of y-values

The interval period between a periodic function's repeats

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.

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.

The ray on the

x-axis

An angle's other ray in standard position

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

Angles with a common terminal side in standard position

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

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

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

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

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

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

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.

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

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.

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

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.

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.

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

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

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

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

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

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

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.

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.

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

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.

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.

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

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

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

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

A numerical or variable array arranged rectangle-wise

A matrix with order m x m

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

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