AP Precalculus Review Flashcards

Vocabulary flashcards for AP Precalculus final exam review, covering key concepts and definitions.

Exponential Functions

Situations involving proportional growth, or repeated multiplication, where the input values change proportionally over equal-length output-value intervals.

Frequency

Indicates how many cycles (or repetitions) a function completes within a given interval; the reciprocal of the period.

Polar Coordinates

A grid of circles centered at the origin and lines through the origin, defined as an ordered pair (r, θ).

Polar Coordinates

Representing points in a plane using a distance from a central point (pole) and an angle from a reference direction (polar axis).

Global/Absolute Minimum

The least of all local minima.

Exponential Growth

A function that is always increasing, with the function equation f(x) = ab^x when a > 0 and b > 1.

Function

A mathematical relation that maps a set of input values to a set of output values such that each input value is mapped to exactly one output value.

Sinusoidal Functions

Any function that involves additive and multiplicative transformations of f(θ) = sin θ.

Polar Roses

A polar curve that resembles a flower with petals, defined by r = a sin(nθ) or r = a cos(nθ).

Degree of a Polynomial

The largest exponent of a polynomial function.

Amplitude

The distance from the midline to either the maximum or minimum value of the function.

Point of Inflection

Points of a polynomial function where the rate of change changes from increasing to decreasing or vice versa.

Tangent

The ratio of the angle's sine to its cosine.

Logarithmic Functions

The input values of this function change proportionately as output values increase in equal-length intervals.

Exponential Function

A function that is always increasing or decreasing and whose graphs are always concave up or concave down, without points of inflection, with the function equation f(x) = ab^x.

Cosine

The x-coordinate of point P in the unit circle.

Logarithmic Models

Any function representation that is equivalent to the analytical form.

Increasing Function

As the input values increase, the output values always increase in the interval of its domain.

Midline

A horizontal line that represents the average value of the function, halfway between its maximum and minimum values.

Tangent

In a right-angled triangle, it represents the ratio of the length of the opposite side to the length of the adjacent side of an angle.

Horizontal Asymptote

If the polynomial p(x) = ax^n+… in the numerator has the same degree n as the denominator q(x) = bx^n+…, the equation of the asymptote is y=a/b.

Horizontal Asymptote

If a polynomial in the numerator has a degree smaller than that of denominator, the equation of the asymptote is y = 0.

Pythagorean Trigonometric Identity

sin²θ + cos²θ is equal to 1.

Rational Function

The quotient of two polynomial functions.

Slant Asymptote

If a polynomial in the numerator has a degree one larger than the degree of denominator, the result of long or synthetic division will be a quotient of y = mx + b and a remainder.

Conversion form Rectangular Coordinates to Polar Coordinates

r = √(x²+y²) and θ = arctan (y/x). The angle θ is typically measured in radians and must be adjusted based on the quadrant of the point (x,y).

Polynomial Function

p(n) = anx^n + a{n-1}x^{n-1} + a{n-2}x^{n-2} + … + a2x^2 + a1x + a0, where n is a positive integer, ai is a real number for each i from 1 to n, and an is nonzero.

Exponential Decay

This function is always decreasing. The function equation is f(x) = ab^x when a > 0 and 0 < b < 1.

Concave up

When the average rate of change over equal-length input-value intervals is increasing for all small-length intervals.

Geometric Sequence

A special type of sequence where the ratio of every two successive terms is a constant.

Arithmetic Sequence

A special type of sequence where the difference between consecutive terms is always the same.

Period

The smallest positive value k such that f(x + k) = f(x) for all x in the domain.

Multiplicity

When a linear factor (x - a) is repeated n times, the corresponding zero of the polynomial function is repeated n times.

Sine

The y-coordinate of point P in the unit circle.

Decreasing Function

As the input values increase, the output values always decrease in the interval of its domain.

Additive Transformation

Transformation of a function f that results in a vertical or horizontal translation of the graph of f.

Composition of Functions

(f ∘ g)(x) = f(g(x)) maps a set of input values to a set of output values such that the output value of g are used as input values of f.

Polar Limaçons

A type of polar curve described by the general equation r = a + b cos(θ) or r = a + b sin(θ).

Concave down

When the average rate of change over equal-length input-value intervals is decreasing for all small-length intervals.

Vertical Asymptote

Occurs at x=a if the multiplicity of a as a real zero in the denominator is greater than its multiplicity as a real zero in the numerator.

Inverse Functions

f is invertible if each output value of f is mapped from a unique input value.

Negative rate of change

Indicates that as one quantity increases, the other decreases.

Global/Absolute Maximum

The greatest of all local maxima.

Inverse Trigonometric Functions

The input and output values are switched from their corresponding trigonometric functions.

Conversion form Polar to Rectangular coordinates

x = r cosθ and y = r sin θ.

Multiplicative Transformation

Transformation of a function f that results in a vertical or horizontal dilation of the graph of f.

Positive rate of change

Indicates that as one quantity increases, the other quantity does the same.

End Behavior of a polynomial function

As input values of a nonconstant polynomial function increase or decrease without bound, the output values will either increase or decrease without bound.