Mathematics Review Flashcards

This set of flashcards covers key vocabulary and concepts in mathematics related to polynomial functions, trigonometry, logarithms, and functions.

Solving polynomial inequalities

The process of finding the values of the variable that make a polynomial inequality true.

Multiplying and conjugate with 'i'

The multiplication of complex numbers involving the imaginary unit, often used to simplify expressions.

Difference quotient

The formula used to find the average rate of change of a function between two points.

All forms of linear equations

Different representations of linear equations, including slope-intercept, point-slope, and standard forms.

Transformations of a quadratic function

Changes to the graph of a quadratic function, such as shifts, stretching, and reflections.

Average rate of change

The change in the value of a function divided by the change in its input over an interval.

Evaluating from a piecewise function

The process of finding the value of a function defined by multiple sub-functions based on the input.

Function composition

The process of combining two functions by substituting one into the other.

Right triangle trigonometry

The study of relationships in right triangles, particularly involving sine, cosine, and tangent.

Midpoint formula

A formula to find the midpoint of a line segment, given its endpoints.

X intercepts and multiplicity ideas

The points where a function intersects the x-axis, along with concepts of how many times it touches or crosses.

Parallel lines (equations)

Mathematical expressions that represent two lines that never meet and have equal slopes.

Subtracting functions

The operation of taking one function and subtracting another, resulting in a new function.

Synthetic division to factor a polynomial

A method used to divide polynomials more easily, particularly when the divisor is of the form x - c.

Inverse functions

Functions that reverse the effect of the original function, such that f(f^(-1)(x)) = x.

Domain of a rational function with square root

The set of all possible inputs (x-values) for which the rational function is defined, particularly avoiding division by zero and negative roots.

Quadratic function from a graph

A technique to derive the equation of a quadratic function based on its graph.

End behavior of a polynomial function

The behavior of the graph of a polynomial function as the input approaches positive or negative infinity.

Even or Odd functions

Functions whose graphs are symmetric about the y-axis (even) or origin (odd).

The imaginary unit 'i' with multiplying radicals

Refers to the application of the imaginary unit i, defined as the square root of -1, in operations with radicals.

Polynomial function from zeros

Constructing a polynomial function based on its roots or zeros.

Asymptotes of a rational function

Lines that the graph of a rational function approaches but never touches or crosses.

Graphing a rational function to become linear with hole

The technique of identifying points on a graph of a rational function that become linear after removing a hole.

Slant asymptotes

Oblique lines that a rational function approaches as x approaches infinity, different from vertical or horizontal asymptotes.

Domain of a radical expression (factoring)

Determining the allowable values for the input of a radical expression based on factoring.

Natural logarithm properties

Rules and characteristics regarding the natural logarithm, such as ln(e) = 1.

Special right triangle properties

Properties relating to the angles and sides of special right triangles, including 30-60-90 and 45-45-90 triangles.

Linear and Angular speeds

Measurements of speed in terms of linear distance per time and angular distance per time, respectively.

Arc length

The distance along a curve or circular path, calculated based on the angle subtended at the center.

Unit circle values

Values of sine, cosine, and tangent for angles represented on the unit circle.

Cofunction identities

Trigonometric identities that relate the sine and cosine functions to their complementary angles.

Expand and condense logarithmic expressions

Techniques for rewriting logarithmic expressions into expanded or condensed forms.