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Questions and Answers

What is the Absolute Value?

The average of a set of numbers

The square of a number

The highest value in a set

It's distance from the number line (correct)

What is an Empty Set?

The solutions set of an equation that has no solution.

What does Set Builder Notation express?

The expression of the solution set of an inequality.

What is Interval Notation?

Using the infinitive symbols to indicate that the solution set of an inequality is unbounded. Signup and view all the answers

What is a Compound Inequality?

Two inequalities joined by the word 'and' or 'or'. Signup and view all the answers

What does Intersection refer to in inequalities?

The graph of a compound inequality containing 'and'. Signup and view all the answers

What does Union refer to in inequalities?

The graph of a compound inequality containing 'or'. Signup and view all the answers

What is an Ordered Pair?

A pair of coordinates written in the form (x, y). Signup and view all the answers

What is a Cartesian Coordinate Plane?

A plane divided into four quadrants. Signup and view all the answers

What are Quadrants in a coordinate plane?

The four areas of a coordinate plane. Signup and view all the answers

What is a Relation in mathematics?

A set of ordered pairs. Signup and view all the answers

What is the Domain of a relation?

The set of all x-coordinates of a relation. Signup and view all the answers

What is the Range of a relation?

The set of all y-coordinates of a relation. Signup and view all the answers

What is a Function?

A relation in which each element of the domain is paired with exactly one element of the range. Signup and view all the answers

What is Mapping in a function?

How each member of the domain is paired with each member of the range. Signup and view all the answers

What is a One-to-One Function?

A function where each element of the range is paired with exactly one element of the domain. Signup and view all the answers

The Vertical Line Test determines if a graph represents a function.

True Signup and view all the answers

What is an Independent Variable?

In a function, the variable, usually x, whose values make up the domain. Signup and view all the answers

What is a Dependent Variable?

The other variable in a function, usually y, whose values depend on x. Signup and view all the answers

What is Function Notation?

An equation of y in terms of x can be rewritten so that y = f(x). Signup and view all the answers

What is Slope?

The ratio of the change in y-coordinates to the change in x-coordinates. Signup and view all the answers

What is Rate of Change?

How much a quantity changes on average relative to the change in another quantity, often time. Signup and view all the answers

What is a Family of Graphs?

A group of graphs that displays one or more similar characteristics. Signup and view all the answers

What is a Parent Graph?

The simplest of graphs in a family. Signup and view all the answers

What are Parallel Lines?

Non-vertical coplanar lines with the same slope. Signup and view all the answers

What are Perpendicular Lines?

In a plane, any two oblique lines the product of whose slopes is -1. Signup and view all the answers

What is Point-Slope Form?

An equation in the form y - y1 = m(x - x1). Signup and view all the answers

What is Slope-Intercept Form?

The equation of a line in the form y = mx + b. Signup and view all the answers

What is Standard Form?

An angle positioned so that its vertex is at the origin and its initial side is along the positive x-axis. Signup and view all the answers

Study Notes

Algebra 2 Key Concepts

Absolute Value
- Represents the distance of a number from zero on the number line.
Empty Set
- Indicates a solutions set for an equation with no valid solutions.
Set Builder Notation
- A way to denote the solution set of inequalities through a concise expression.
Interval Notation
- Expresses unbounded solution sets of inequalities using infinite symbols.
Compound Inequality
- Joins two inequalities with "and" or "or," reflecting their combined solutions.
Intersection
- Represents the region satisfying both parts of a compound inequality using "and."
Union
- Represents the combined solutions of a compound inequality using "or."
Ordered Pair
- Coordinates presented as (x, y), representing points on a Cartesian plane.
Cartesian Coordinate Plane
- Divided into four quadrants, facilitating the location of points.
Quadrants
- The four sections of the Cartesian plane, each representing different signs of x and y.
Relation
- A collection of ordered pairs showcasing associations between elements.
Domain
- The complete collection of x-coordinates within a relation.
Range
- The total set of y-coordinates corresponding to the domain in a relation.
Function
- A specific type of relation where each input (domain) has a unique output (range).
Mapping
- Describes the relationship between members of the domain and their matched outputs in the range.
One-to-One Function
- A function where each element of the range is linked to one unique element from the domain.
Vertical Line Test
- A graphical method to determine if a relation is a function; a vertical line should intersect the graph at most once.
Independent Variable
- Typically represented as x; values constituting the domain in a function.
Dependent Variable
- Usually represented as y; values depend on the corresponding x values in the function.
Function Notation
- A representation of equations where y can be expressed as f(x).
Slope
- Calculated as the ratio of vertical change in y-coordinates to horizontal change in x-coordinates.
Rate of Change
- Measures the frequency or degree of change in one quantity in response to changes in another, often related to time.
Family of Graphs
- A collection of graphs sharing common characteristics or behaviors.
Parent Graph
- The most basic form of a graph in a family, serving as a foundational model.
Parallel Lines
- Lines in the same plane that never meet, characterized by identical slopes.
Perpendicular Lines
- Lines intersecting at a right angle, where the product of their slopes equals -1.
Point-Slope Form
- Used to express linear equations in the form y - y1 = m(x - x1), where m is the slope.
Slope-Intercept Form
- Represents linear equations in the format y = mx + b, with m as the slope and b as the y-intercept.
Standard Form
- Refers to a specific layout of equations, often starting at the origin with the initial side along the positive x-axis.