Algebra I: Chapter 3 Flashcards

Questions and Answers

What is a dependent variable?

The variable in a relation with a value that depends on the value of the independent variable.

What is a function?

A relationship between input and output where there is exactly one output for each input.

What is an independent variable?

The value of the variable in a relation that determines the output.

What is a linear equation?

An equation in which the variables appear in separate terms and neither variable contains an exponent other than 1. Signup and view all the answers

What is a linear function?

It is a function in which the graph of the solutions forms a straight line. Signup and view all the answers

What is the vertical line test?

If any vertical line drawn on the graph of a relation passes through no more than one point on the graph for each value of x in the domain, then the relation is a function. Signup and view all the answers

What is another name for the coordinate plane?

Coordinate system. Signup and view all the answers

What is a domain in mathematics?

The set of all x-coordinates from each ordered pair. Signup and view all the answers

What is an ordered pair?

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

What is the origin in a coordinate system?

The point at which the number lines intersect. Signup and view all the answers

What is a range in mathematics?

The set of all y-coordinates from each ordered pair. Signup and view all the answers

What is a relation?

A set of ordered pairs, which can be represented as an equation, a graph, a table, or with mapping. Signup and view all the answers

What is the x-axis?

The horizontal number line that helps to form the coordinate system. Signup and view all the answers

What is the y-axis?

The vertical number line that helps to form the coordinate system. Signup and view all the answers

What is mapping in mathematics?

It illustrates how each element of the domain is paired with an element in the range. Signup and view all the answers

What is a discrete function?

A graph that consists of points that are not connected. Signup and view all the answers

What is a continuous function?

A function graphed with a line or a smooth curve. Signup and view all the answers

What is function notation?

f(x) = 3x - 8 Signup and view all the answers

What is a nonlinear function?

A function with a graph that is not a straight line. Signup and view all the answers

What is an exponential function?

A function that can be described by an equation of the form y = a to the x power, where a > 0 and a does NOT equal 1. Signup and view all the answers

What is a parabola?

The graph of a quadratic function. Signup and view all the answers

What is a quadratic function?

An equation of the form y = ax² + bx + c, where a ≠ 0. Signup and view all the answers

Study Notes

Key Concepts in Relations, Functions, and Graphing

Dependent Variable: Its value is influenced by the independent variable in a relation.
Function: A specific type of relation; each input is associated with exactly one output.
Independent Variable: The variable that determines the output’s value in a functions’ relation.

Types of Equations and Functions

Linear Equation: Contains variables without exponents other than 1; graphs to a straight line.
Linear Function: A function whose graph results in a straight line, representing a constant rate of change.
Nonlinear Function: A function whose graph does not form a straight line, indicating a variable rate of change.

Graphing Essentials

Vertical Line Test: A method to verify if a relation is a function; any vertical line should intersect the graph at most once per x-value.
Coordinate Plane: The grid where points are plotted, formed by intersecting horizontal (x-axis) and vertical (y-axis) number lines.
Ordered Pair: A coordinate representation in the form (x, y), indicating a point's position on the plane.

Components of Functions

Domain: The complete set of x-coordinates (input values) from all ordered pairs in a function.
Range: The complete set of y-coordinates (output values) derived from the range of the independent variable.
Origin: The central point (0,0) on the coordinate plane where the x-axis and y-axis intersect.

Types of Functions

Discrete Function: Represented by separate points; the graph does not connect them.
Continuous Function: Illustrated by a smooth line or curve; indicates a complete range of values.
Exponential Function: Function expressed as y = a^x, where a is a positive constant not equal to one.
Quadratic Function: Defined by the form y = ax² + bx + c, with the coefficient 'a' being non-zero.

Additional Concepts

Function Notation: A way to denote functions using symbols, such as f(x) = 3x - 8.
Mapping: A visual representation showing how each value in the domain relates to a value in the range.
Parabola: The graphical representation of quadratic functions typically U-shaped.

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Test your understanding of key concepts in relations, functions, and graphing with these flashcards. Each card defines important terms you'll encounter in Chapter 3 of Algebra I. Perfect for quick reviews before exams!