AP Precalculus - Unit 1: Polynomial and Rational Functions Flashcards

Function

Function

A mathematical relationship 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.

Input Values

Also known as the domain or independent variable (x), these are the values that are used as input in a function.

Output Values

Also known as the range or dependent variable (y), these are the values that are produced as output by a function.

Function Rule

The rule that determines how the input values are transformed into output values in a function.

Increasing Function

A function is increasing over an interval of its domain if, as the input values increase, the output values always increase.

Decreasing Function

A function is decreasing over an interval of its domain if, as the input values increase, the output values always decrease.

Graph

A visual display of input-output pairs that shows how values vary in a function.

Concave Up

A rate of change is increasing in a function.

Concave Down

A rate of change is decreasing in a function.

x-intercepts

The zeros of the function, which are the values of x for which the function equals zero.

Average Rate of Change

The average rate of change over a closed interval [a, b] is the slope of the secant line from the point (a, f(a)) to (b, f(b)).

Positive Rate of Change

When one quantity increases, the other quantity increases as well.

Negative Rate of Change

When one quantity increases, the other quantity decreases.

Local/Relative Maximum/Minimum

Points where a polynomial changes between increasing and decreasing or includes an endpoint with restricted domain.

Global/Absolute Maximum/Minimum

The greatest local maximum or least local minimum in a polynomial.

Points of Inflection

Points where the rate of change of a function changes from increasing to decreasing or from decreasing to increasing, resulting in a change in concavity.

Complex Numbers

Numbers that include both real numbers and non-real numbers.

Real Zeros

Zeros of a polynomial that are real numbers.

Even Function

A function that is symmetric over the line x = 0 and satisfies the property f(-x) = f(x).

Odd Function

A function that is symmetric over the point (0, 0) and satisfies the property f(-x) = -f(x).

End Behavior

The behavior of a function as the input values increase or decrease without bound.

Rational Function

The ratio of two polynomials where the polynomial in the denominator is not equal to zero.

Vertical Asymptote

Zeros of the polynomial in the denominator that are not zeros of the numerator.

Hole

A point where a zero appears more times in the numerator than the denominator in a rational function.

Equivalent Representations

Different forms of expressing polynomial and rational expressions, such as standard form and factored form.

Polynomial Long Division

A method used to find the equations of slant asymptotes of graphs of rational functions.

Binomial Theorem

A theorem used to expand terms in the form (a + b)^n and polynomials functions in the form of (x + c)^n.

Transformations of Functions

Changes made to a parent function, such as vertical or horizontal translations, dilations, or reflections.

Function Model Selection

Choosing the appropriate type of function model based on the characteristics of the data or scenario.

Assumptions and Restrictions

The assumptions made and restrictions applied when constructing a function model.

Function Model Construction

The process of creating a function model based on restrictions, transformations, technology, or piece-wise functions.

Application of Function Models

Using function models to draw conclusions about data sets or scenarios and making appropriate use of units of measure.