Graphing Concepts in Algebra 1

Questions and Answers

What is a continuous graph?

A graph with breaks in it

A visual test for functions

A graph with no breaks in it (correct)

A graph of isolated points

What is a relation in mathematics?

The mapping between a set of inputs and a set of outputs.

Define domain.

The set of all input values in a relation.

Define range.

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

What is a discrete graph?

A graph of isolated points Signup and view all the answers

What does the vertical line test determine?

Whether a relation represented as a graph is a function. Signup and view all the answers

Define function.

A relation between a given set of elements for which each input value there exists exactly one output value. Signup and view all the answers

What is function notation?

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

What characterizes an increasing function?

It increases across the entire domain Signup and view all the answers

What is a decreasing function?

It decreases across the entire domain Signup and view all the answers

What characterizes a constant function?

It does not change or remains constant 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 that create a straight line and include functions of the form f(X)=mx+b. Signup and view all the answers

Define exponential functions.

Functions of the form f(x)=axb^2, where a and b are real numbers. Signup and view all the answers

What is an absolute minimum?

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

What is a dependent quantity?

When one quantity depends on another in a problem situation. Signup and view all the answers

Define independent quantity.

The quantity that the dependent quantity depends upon. Signup and view all the answers

What is an absolute maximum?

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

Define linear absolute value.

The absolute value of a number is its distance from zero on the number line. Signup and view all the answers

What are linear piecewise functions?

Functions that have equation changes for different parts or pieces of the domain. Signup and view all the answers

Define quadratic functions.

Functions in the form of f(x)=ax^2+bx+c where a, b, and c are real numbers and a is not equal to zero. Signup and view all the answers

Study Notes

Graphing Concepts in Algebra 1

Continuous Graph: Characterized by no breaks or interruptions; represents a smooth connection between points.
Relation: A systematic pairing of input values (domain) with output values (range).
Domain: The complete set of all possible input values in a given relation.
Range: The complete set of all possible output values corresponding to the inputs in a relation.
Discrete Graph: Composed of distinct, isolated points rather than connected lines.
Vertical Line Test: A method for determining if a graph is a function; if any vertical line intersects the graph more than once, it is not a function.
Function: A specific relation where each input has a unique output; crucial for defining mathematical operations.
Function Notation: A standardized way of expressing functions algebraically, frequently using symbols like f(x).

Types of Functions

Increasing Function: A function where the output values rise as the input values increase across the entire domain.
Decreasing Function: A function where the output values decline as the input values increase across the entire domain.
Constant Function: A function whose output remains unchanged regardless of input variability.
Function Family: A collection of functions that share common features or behaviors.
Linear Functions: Functions that produce straight-line graphs, typically represented in the form f(x) = mx + b, where m and b are real numbers.
Exponential Functions: Functions in the form f(x) = a * b^(x), where a and b are real numbers, b is greater than zero, and b is not equal to one.

Function Characteristics

Absolute Minimum: The lowest point on a graph, characterized by the smallest y-coordinate compared to all other points.
Dependent Quantity: A variable whose value is determined by another variable; reflects the outcome of a function.
Independent Quantity: The variable that influences or determines the value of the dependent quantity.
Absolute Maximum: The highest point on a graph, characterized by the largest y-coordinate among all points.
Linear Absolute Value: Represents the distance of a number from zero on the number line, reflecting its non-negative value.
Linear Piecewise Function: Functions defined by multiple equations, each applicable to different segments of the domain.
Quadratic Functions: Functions that follow the standard form f(x) = ax² + bx + c, where a, b, and c are real numbers and a is non-zero, typically producing parabolic graphs.

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Description

This quiz covers essential graphing concepts in Algebra 1, including definitions and characteristics of continuous and discrete graphs. You will also explore key terms such as functions, domain, range, and the vertical line test. Test your understanding of these foundational concepts in algebra.