Algebra 1 Honors Module 1 Vocabulary

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Questions and Answers

What is a dependent quantity?

The set of input values.
The quantity that depends on another in a problem situation. (correct)
The quantity that the dependent quantity depends on.
The mapping between a set of input values and a set of output values.

What is an independent quantity?

The set of input values.
The quantity that depends on another in a problem situation.
The quantity that the dependent quantity depends on. (correct)
The mapping between a set of input values and a set of output values.

What is a relation?

The mapping between a set of input values and a set of output values.

What does the domain of a function represent?

The set of input values. Signup and view all the answers

What is a range in mathematics?

The set of output values. Signup and view all the answers

Define a function.

A relation between a given set of elements, such that for each element in the domain there exists exactly one element in the range. Signup and view all the answers

What is the vertical line test?

A visual method used to determine whether a relation represented as a graph is a function. Signup and view all the answers

What does a discrete graph represent?

A graph of isolated points. Signup and view all the answers

What is a continuous graph?

A graph of points that are connected by a line or smooth curve with no breaks in the graph. Signup and view all the answers

What is the purpose of function notation?

A way of representing functions algebraically. Signup and view all the answers

What characterizes an increasing function?

Both the independent variable and the dependent variable increase across the entire domain. Signup and view all the answers

What is a decreasing function?

A function where both the independent variable and the dependent variable decrease across the entire domain. Signup and view all the answers

Define a constant function.

A function where the dependent variable does not change over the entire domain. Signup and view all the answers

What is a function family?

A group of functions that share certain characteristics. Signup and view all the answers

What are linear functions?

Functions whose graph is a line. Signup and view all the answers

Define exponential functions.

Functions in which the independent variable appears as an exponent. Signup and view all the answers

What is an absolute minimum in a function?

A point on the graph of a function that has a y-coordinate that is less than the y-coordinate of every other point on the graph. Signup and view all the answers

What does absolute maximum refer to?

A point on the graph of a function that has a y-coordinate that is greater than the y-coordinate of every other point on the graph. Signup and view all the answers

What are quadratic functions?

Functions whose graphs are smooth u-shaped curves. Signup and view all the answers

Define linear absolute value functions.

Functions whose graphs are composed of two lines that make a v shape. Signup and view all the answers

What are linear piecewise functions?

Functions with equations that change for different parts, or pieces, of the domain. Signup and view all the answers

What is an x-intercept?

The point where the graph crosses the x-axis. Signup and view all the answers

What is a y-intercept?

The point where the graph crosses the y-axis. Signup and view all the answers

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Study Notes

Key Terms in Algebra 1 Honors

Dependent Quantity: The variable in a problem that relies on another variable.
Independent Quantity: The variable that influences the dependent quantity in a problem.

Relations and Their Components

Relation: A method of pairing input values with corresponding output values.
Domain: The complete set of input values for a relation.
Range: The complete set of output values that correspond to the domain.

Functions and Their Properties

Function: A specific type of relation where each input (from the domain) corresponds to exactly one output (in the range).
Function Notation: A notation system to express functions algebraically for easy identification of variables.
Vertical Line Test: A graphical method to determine if a relation is a function by checking if vertical lines intersect the graph at more than one point.

Graph Types

Discrete Graph: Represents data using distinct, separate points.
Continuous Graph: Consists of points connected by lines or curves, with no breaks.

Function Behavior

Increasing Function: A function where the dependent quantity rises as the independent quantity increases over the entire domain.
Decreasing Function: A function where both the independent and dependent quantities decline through the domain.
Constant Function: A function that maintains the same output regardless of the independent variable’s value.

Function Families

Function Family: A collection of functions sharing similar properties.
Linear Functions: Functions that graph as straight lines.
Exponential Functions: Functions where the independent variable acts as an exponent.
Quadratic Functions: Functions characterized by smooth, U-shaped graphs.
Linear Absolute Value Functions: Functions whose graphs form a V-shape due to the absolute value.
Linear Piecewise Functions: Functions composed of different linear equations based on specific intervals of the domain.

Important Points on Graphs

Absolute Minimum: The lowest point in the graph, marked by the least y-coordinate.
Absolute Maximum: The highest point in the graph, characterized by the greatest y-coordinate.
X-Intercept: The point at which the graph intersects the x-axis.
Y-Intercept: The point at which the graph intersects the y-axis.

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