AP Precalculus - Unit 1: Polynomial and Rational Functions Flashcards (copy)

5.0(1)
learnLearn
examPractice Test
spaced repetitionSpaced Repetition
heart puzzleMatch
flashcardsFlashcards
Card Sorting

1/31

Study Analytics
Name
Mastery
Learn
Test
Matching
Spaced

No study sessions yet.

32 Terms

1
New cards

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.

2
New cards

Input Values

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

3
New cards

Output Values

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

4
New cards

Function Rule

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

5
New cards

Increasing Function

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

6
New cards

Decreasing Function

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

7
New cards

Graph

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

8
New cards

Concave Up

A rate of change is increasing in a function.

9
New cards

Concave Down

A rate of change is decreasing in a function.

10
New cards

x-intercepts

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

11
New cards

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)).

12
New cards

Positive Rate of Change

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

13
New cards

Negative Rate of Change

When one quantity increases, the other quantity decreases.

14
New cards

Local/Relative Maximum/Minimum

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

15
New cards

Global/Absolute Maximum/Minimum

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

16
New cards

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.

17
New cards

Complex Numbers

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

18
New cards

Real Zeros

Zeros of a polynomial that are real numbers.

19
New cards

Even Function

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

20
New cards

Odd Function

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

21
New cards

End Behavior

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

22
New cards

Rational Function

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

23
New cards

Vertical Asymptote

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

24
New cards

Hole

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

25
New cards

Equivalent Representations

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

26
New cards

Polynomial Long Division

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

27
New cards

Binomial Theorem

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

28
New cards

Transformations of Functions

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

29
New cards

Function Model Selection

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

30
New cards

Assumptions and Restrictions

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

31
New cards

Function Model Construction

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

32
New cards

Application of Function Models

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