Algebra I: Chapter 3 Flashcards
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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?

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

What is a linear function?

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

What is the vertical line test?

<p>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.</p> Signup and view all the answers

What is another name for the coordinate plane?

<p>Coordinate system.</p> Signup and view all the answers

What is a domain in mathematics?

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

What is an ordered pair?

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

What is the origin in a coordinate system?

<p>The point at which the number lines intersect.</p> Signup and view all the answers

What is a range in mathematics?

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

What is a relation?

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

What is the x-axis?

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

What is the y-axis?

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

What is mapping in mathematics?

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

What is a discrete function?

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

What is a continuous function?

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

What is function notation?

<p>f(x) = 3x - 8</p> Signup and view all the answers

What is a nonlinear function?

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

What is an exponential function?

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

What is a parabola?

<p>The graph of a quadratic function.</p> Signup and view all the answers

What is a quadratic function?

<p>An equation of the form y = ax² + bx + c, where a ≠ 0.</p> 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!

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