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1

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.

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Input Values

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

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Output Values

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

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4

Function Rule

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

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5

Increasing Function

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

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6

Decreasing Function

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

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7

Graph

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

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8

Concave Up

A rate of change is increasing in a function.

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9

Concave Down

A rate of change is decreasing in a function.

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10

x-intercepts

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

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11

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)).

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12

Positive Rate of Change

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

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13

Negative Rate of Change

When one quantity increases, the other quantity decreases.

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14

Local/Relative Maximum/Minimum

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

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Global/Absolute Maximum/Minimum

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

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16

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.

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17

Complex Numbers

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

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18

Real Zeros

Zeros of a polynomial that are real numbers.

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19

Even Function

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

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20

Odd Function

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

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21

End Behavior

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

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22

Rational Function

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

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23

Vertical Asymptote

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

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24

Hole

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

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25

Equivalent Representations

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

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Polynomial Long Division

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

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Binomial Theorem

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

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28

Transformations of Functions

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

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29

Function Model Selection

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

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Assumptions and Restrictions

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

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31

Function Model Construction

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

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Application of Function Models

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

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