AP Precalculus Summer Review Vocabulary

A comprehensive set of vocabulary flashcards covering algebraic, trigonometric, and analytic concepts required for the AP Precalculus summer review assignment.

Linear Function

A function whose graph is a straight line; it can be written in the form f(x)=mx+b, where m is the slope and b is the y-intercept.

Quadratic Function

A polynomial function of degree 2, typically written in standard form as f(x)=ax²+bx+c with a≠0; its graph is a parabola.

Polynomial Function

A function that is the sum of terms of the form an xⁿ, where n is a non-negative integer and coefficients an are real numbers.

Absolute Value Function

A function defined by f(x)=|x|, which outputs the non-negative distance of x from zero; its graph forms a ‘V’ shape.

Piecewise-Defined Function

A function composed of different expressions over separate intervals of the domain.

Domain

The complete set of all possible input (x) values for which a function is defined.

Range

The complete set of all possible output (y) values produced by a function.

Vertex (of a Parabola)

The highest or lowest point on a parabola; located at (−b/2a , f(−b/2a)) in standard form.

Axis of Symmetry

A vertical line that divides a parabola into two mirror-image halves; given by x = −b/2a for quadratics.

Zero (Root) of a Function

An x-value that makes the function equal to zero; corresponds to an x-intercept on the graph.

y-Intercept

The point where a graph crosses the y-axis, found by evaluating the function at x=0.

System of Equations

A set of two or more equations with the same variables that are solved simultaneously.

Quadratic Formula

x = (−b ± √(b²−4ac)) / 2a, used to find the roots of ax²+bx+c=0.

Factoring

Rewriting an expression as a product of its factors to simplify or solve equations.

Exponential Function

A function of the form f(x)=a·b^x where a≠0 and b>0, b≠1; exhibits constant percentage growth or decay.

Radical Expression

An expression that contains a root symbol, such as √x or ³√x.

Complex Number

A number of the form a+bi, where a and b are real and i = √−1.

Imaginary Unit (i)

Defined as √−1; satisfies i² = −1.

Complex Conjugate

For a+bi, the conjugate is a−bi; used to rationalize denominators with complex numbers.

Modulus of a Complex Number

The distance of a+bi from the origin, given by |a+bi| = √(a²+b²).

Logarithm

The inverse of an exponential function; log_b a answers the question, ‘To what power must b be raised to get a?’

Natural Logarithm

A logarithm with base e (≈2.718); written as ln x.

Properties of Logarithms

Rules such as logb(MN)=logb M + logb N, logb(M/N)=logb M − logb N, and logb(M^k)=k·logb M.

Exponent Rules

Algebraic rules for simplifying expressions with powers, e.g., b^m · b^n = b^(m+n) and (b^m)^n = b^(mn).

Rational Function

A function expressed as the ratio of two polynomials, f(x)=P(x)/Q(x), with Q(x)≠0.

Vertical Asymptote

A vertical line x = a where a rational function grows without bound as x approaches a.

Horizontal Asymptote

A horizontal line y = L that the graph of a function approaches as x→±∞.

Slant (Oblique) Asymptote

A non-horizontal, non-vertical line the graph approaches as x→±∞; occurs when numerator degree is exactly one more than denominator degree.

Point of Discontinuity (Hole)

A single x-value where a function is undefined due to a cancelled factor; the graph has a ‘hole.’

Coterminal Angle

Two angles that differ by an integer multiple of 360° (or 2π radians) and share the same initial and terminal sides.

Reference Angle

The acute angle formed between the terminal side of a given angle and the x-axis; used for evaluating trig functions.

Trigonometric Function

One of the six ratios—sine, cosine, tangent, cosecant, secant, cotangent—relating sides of right triangles or coordinates on the unit circle.

Sine (sin)

For angle θ in standard position, sin θ = y/r, where (x,y) is a point on the terminal side and r=√(x²+y²).

Cosine (cos)

For angle θ, cos θ = x/r with (x,y) on the terminal side and r=√(x²+y²).

Tangent (tan)

Defined as tan θ = sin θ / cos θ = y/x, provided cos θ ≠ 0.

Cotangent (cot)

The reciprocal of tangent: cot θ = cos θ / sin θ = x/y, provided sin θ ≠ 0.

Secant (sec)

The reciprocal of cosine: sec θ = 1 / cos θ = r/x, provided cos θ ≠ 0.

Cosecant (csc)

The reciprocal of sine: csc θ = 1 / sin θ = r/y, provided sin θ ≠ 0.

Unit Circle

A circle of radius 1 centered at the origin; used to define trig functions for all real angles.

Period (Trigonometry)

The horizontal length required for a trigonometric function to complete one full cycle.

Amplitude

Half the distance between the maximum and minimum values of a sinusoidal function; represents vertical stretch.

Phase (Horizontal) Shift

A horizontal translation of a trigonometric graph, determined by the value inside the function’s argument.

Vertical Shift

An upward or downward translation of a graph, determined by a constant added outside the function.

Reflection (Graph)

A flip of a graph over an axis, caused by a negative coefficient (e.g., −f(x) reflects across the x-axis).

Extraneous Solution

A solution obtained algebraically that does not satisfy the original equation, often arising from squaring or multiplying both sides.

Radical Equation

An equation in which the variable appears under a radical sign.

Vertex Form of a Quadratic

An expression written as f(x)=a(x−h)²+k, where (h,k) is the vertex.

Intercept (Factored) Form of a Quadratic

An expression written as f(x)=a(x−p)(x−q), where p and q are the x-intercepts.

Standard Form of a Quadratic

The form f(x)=ax²+bx+c, where a, b, and c are real constants and a≠0.

Quadratic Discriminant

The quantity Δ = b²−4ac that determines the number and nature of the roots of a quadratic equation.

End Behavior

The trend of a graph as x→∞ or x→−∞, determined by the leading term of a polynomial.