AP Precalculus Glossary Units 1–4 Vocabulary

Vocabulary flashcards covering the key terms and definitions from Units 1–4 of the AP Precalculus Glossary.

Absolute maximum (absolute extrema)

The greatest value of a function over a given interval.

Absolute minimum (absolute extrema)

The lowest value of a function over a given interval.

Average rate of change

The change in output values for two inputs divided by the change in the inputs.

Concave down

A graph whose average rate of change over equal-length intervals is decreasing; points between two data points lie mostly above the secant line.

Concave up

A graph whose average rate of change over equal-length intervals is increasing; points between two data points lie mostly below the secant line.

Decreasing (function)

For any a < b in an interval, f(a) > f(b).

Domain

The set of all possible input values of a relation.

End behavior

Describes how the outputs of a non-constant polynomial behave (approach ±∞) as the input approaches ±∞.

Rational function

A function that can be written as the quotient of two polynomial functions.

Function

A relation in which each input is mapped to exactly one output.

Increasing (function)

For any a < b in an interval, f(a) < f(b).

Inflection point

An input where the rate of change switches from decreasing to increasing or vice versa.

Interval notation

A way to describe all numbers between two bounds using parentheses (exclusion) and brackets (inclusion).

Linear function

A function whose average rate of change is constant over every input interval.

Quadratic function

A function whose average rates of change over equal-length intervals form a linear pattern.

Range

The set of output values produced by the inputs of a relation.

Rate of change

Change in an output quantity relative to the change in the input quantity.

Relation

A set of ordered pairs.

Relative (local) maximum

An input where a function changes from increasing to decreasing, or an included endpoint with that property.

Relative (local) minimum

An input where a function changes from decreasing to increasing, or an included endpoint with that property.

Zero (of a function)

An input where the output equals zero; the graph intersects the x-axis at its zeros.

Argument of a function

The input (independent variable); for logarithms, the expression inside the parentheses.

Arithmetic sequence

A discrete function whose successive terms have a common difference.

Composition of functions

Using the output of one function as the input of another; written (f ∘ g)(x) = f(g(x)).

Exponential function

A non-constant function whose outputs are proportional over equal-length input intervals.

Geometric sequence

A discrete function whose successive terms have a common ratio.

Inverse function

A reverse mapping f⁻¹ where if f(a)=b, then f⁻¹(b)=a on an invertible domain.

Logarithmic function

A function in which inputs change proportionally over equal-length output intervals.

Regression

A method for finding an equation that best fits a set of data points.

Residual

Observed y − predicted y from a regression line; positive above the line and negative below.

Semi-log plot

A graph with one axis on a logarithmic scale and the other on a linear scale.

Periodic function

A function whose outputs repeat a pattern over successive equal-length input intervals.

Period

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

Standard Position Angle

An angle with its vertex at the origin and its initial side along the positive x-axis.

Coterminal angles

Angles in standard position that share the same terminal ray.

Sine

For an angle in standard position, the ratio of the vertical displacement of point P on a circle to the distance of P from the origin.

Cosine

For an angle in standard position, the ratio of the horizontal displacement of point P from the y-axis to the distance of P from the origin.

Tangent

For an angle in standard position, the slope of its terminal ray.

Sinusoidal function

Any function obtained by additive and multiplicative transformations of f(θ)=sin θ.

Amplitude

Half the difference between a sinusoid’s maximum and minimum output values.

Midline (sinusoidal axis)

The horizontal line midway between the maximum and minimum outputs of a sinusoid.

Secant

The reciprocal of cosine, sec x = 1/cos x, where cos x ≠ 0.

Cosecant

The reciprocal of sine, csc x = 1/sin x, where sin x ≠ 0.

Cotangent

The reciprocal of tangent, cot x = 1/tan x, where tan x ≠ 0.

Polar coordinate system

Represents points by (r, θ), where |r| is the radius from the origin and θ is an angle in standard position.

Complex number

A point in the complex plane; rectangular form a+bi or polar form r cos θ + i sin θ.

Parametric function

A pair of equations expressing x and y as functions of a single parameter t.

Parabola

A curve with vertex (h,k); x–h = a(y–k)² (opens left/right) or y–k = a(x–k)² (opens up/down) where a ≠ 0.

Circle

The set of points equidistant r from (h,k); equation (x–h)²+(y–k)² = r².

Ellipse

All points where (x–h)²/a² + (y–k)²/b² = 1; a circle is the special case a = b.

Hyperbola

Set of points satisfying (x–h)²/a² – (y–k)²/b² = 1 (horizontal) or (y–k)²/a² – ( x–h)²/b² = 1 (vertical).