WGU Precalculus Midterm Vocabulary Study Set

Vocabulary practice flashcards covering terminology, formulas, graphical properties, and rules from WGU Precalculus Modules 1–7 and the Midterm review session.

Polynomial

An expression consisting of one or more terms involving mathematical operations.

Like Terms

Terms that have the exact same variable factors raised to the same exponents, allowing their coefficients to be combined.

Profit Function

An application function calculated as $\text{Profit function} = \text{Revenue function} - \text{Cost function}$.

Equation

A mathematical statement of equality.

Relation

A set of ordered pairs $(x, y)$

Domain

The set of all input values or $x$-values in a relation or function.

Range

The set of all output values or $y$-values in a relation or function.

Function

A special relation where each input corresponds to exactly one output.

Vertical Line Test

A visual test on a graph establishing that it represents a function if and only if every vertical line intersects the graph at most once.

Function Composition

An operation where one function is evaluated using the output of another function, denoted as $f(g(x))$.

Rational Function

A function defined by a polynomial divided by another polynomial, with the independent variable in the denominator.

Vertical Asymptote

A vertical line on a graph occurring at input values that make the denominator of a rational function equal to zero.

One-to-One Function

A function in which each output corresponds to exactly one input, resulting in no repeated output values.

Horizontal Line Test

A visual test used to determine if a function is one-to-one, requiring that every horizontal line intersects the graph at most once.

Inverse Function

A function denoted $f^{-1}(x)$ that reverses the input/output relationship of a one-to-one function $f(x)$, satisfying $f^{-1}(b) = a$ whenever $f(a) = b$.

Linear Equation

An equation in which the variable is raised to the first power, graphing as a straight line.

Slope

A measure of line steepness defined as $\frac{\text{change in } y}{\text{change in } x}$ or $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Slope-Intercept Form

The standard linear form $y = mx + b$, where $m$ represents the slope and $b$ represents the y-intercept.

Point-Slope Form

The equation of a line written as $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is a point on the line.

Independent System

A system of linear equations that has exactly one solution.

Inconsistent System

A system of linear equations that has no solution because the lines are parallel.

Dependent System

A system of linear equations that has infinitely many solutions because the lines are coincident or identical.

Quadratic Function

A second-degree polynomial function whose highest exponent on the variable is $2$, which graphs as a parabola.

Vertex

The turning point $(h, k)$ of a parabola, representing a minimum when $a > 0$ or a maximum when $a < 0$.

Axis of Symmetry

The vertical line $x = h$ passing through the vertex of a parabola.

Difference of Perfect Squares

A factoring pattern represented by the algebraic identity $a^2 - b^2 = (a - b)(a + b)$

Vertex Form

The form of a quadratic function given by $f(x) = a(x - h)^2 + k$.

Quadratic Formula

The formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ used to solve any quadratic equation in the form $ax^2 + bx + c = 0$ where $a \neq 0$.

Vertical Shift

A graph transformation outside the function $g(x) = f(x) + k$ that shifts the graph up when $k > 0$ or down when subtracting a positive value.

Horizontal Shift

A graph transformation inside the function where $f(x - h)$ shifts the graph right $h$ units and $f(x + h)$ shifts the graph left $h$ units.

Even Function

A function symmetric about the y-axis that satisfies $f(-x) = f(x)$ for all $x$ in its domain.

Odd Function

A function symmetric about the origin that satisfies $f(-x) = -f(x)$ for all $x$ in its domain.

Symmetry About the Origin

A graphical property where for every point $(x, y)$ on the graph, the point $(-x, -y)$ is also present.

Symmetry About the y-Axis

A graphical property where for every point $(x, y)$ on the graph, the point $(-x, y)$ is also present.

Symmetry About the x-Axis

A graphical property where for every point $(x, y)$ on the graph, the point $(x, -y)$ is also present (which generally does not represent a function).

Market Equilibrium Point

The point on a graph where a supply function and a demand function intersect.

Breakeven Points

Points in a business model where total cost equals total revenue, or where the profit function equals zero ($p(x) = 0$).

Required WGU Midterm Exam Materials

The mandatory proctoring equipment consisting of an external webcam, a calculator, and a small whiteboard with an erasable marker and eraser.