independent variable

(noun)

An independent variable in an equation or function is one whose value is not dependent on any other in the equation or function.

Related Terms

  • quadrant
  • -axis
  • y-axis
  • x-axis
  • ndependent and Dependent Variables
  • graph
  • The logarithmic equation can be converted into the exponential equation .
  • dependent variable
  • quadratic function
  • logarithm
  • vertex
  • parabola
  • ordered pair
  • quadratic

(noun)

The input of a function that can be freely varied.

Related Terms

  • quadrant
  • -axis
  • y-axis
  • x-axis
  • ndependent and Dependent Variables
  • graph
  • The logarithmic equation can be converted into the exponential equation .
  • dependent variable
  • quadratic function
  • logarithm
  • vertex
  • parabola
  • ordered pair
  • quadratic

(noun)

Any variable in an equation or function whose value is not dependent on any other in the equation or function.

Related Terms

  • quadrant
  • -axis
  • y-axis
  • x-axis
  • ndependent and Dependent Variables
  • graph
  • The logarithmic equation can be converted into the exponential equation .
  • dependent variable
  • quadratic function
  • logarithm
  • vertex
  • parabola
  • ordered pair
  • quadratic

(noun)

An arbitrary input; on the Cartesian plane, the value of $x$.

Related Terms

  • quadrant
  • -axis
  • y-axis
  • x-axis
  • ndependent and Dependent Variables
  • graph
  • The logarithmic equation can be converted into the exponential equation .
  • dependent variable
  • quadratic function
  • logarithm
  • vertex
  • parabola
  • ordered pair
  • quadratic

Examples of independent variable in the following topics:

  • Graphical Representations of Functions

    • Functions have an independent variable and a dependent variable.
    • When we look at a function such as $f(x)=\frac{1}{2}x$, we call the variable that we are changing, in this case $x$, the independent variable.
    • We assign the value of the function to a variable, in this case $y$, that we call the dependent variable.  
    • We choose a few values for the independent variable, $x$.  
    • Start by choosing values for the independent variable, $x$.
  • What is a Quadratic Function?

    • where $a$, $b$, and $c$ are constants and $x$ is the independent variable.  
    • With a quadratic function, pairs of unique independent variables will produce the same dependent variable, with only one exception (the vertex) for a given quadratic function.
  • Stretching and Shrinking

    • Multiplying the independent variable $x$ by a constant greater than one causes all the $x$ values of an equation to increase.
    • If the independent variable $x$ is multiplied by a value less than one, all the x values of the equation will decrease, leading to a "stretched" appearance in the horizontal direction.  
  • Graphs of Exponential Functions, Base e

    • The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change (i.e., percentage increase or decrease) in the dependent variable.
  • The Cartesian System

    • A Cartesian plane is particularly useful for plotting a series of points that show a relationship between two variables.
    • Therefore, the revenue is the dependent variable ($y$), and the number of cars is the independent variable ($x$).  
  • Graphing Equations

    • For an equation with two variables, $x$ and $y$, we need a graph with two axes: an $x$-axis and a $y$-axis.
    • We'll start by choosing a few $x$-values, plugging them into this equation, and solving for the unknown variable $y$.
    • Input values (for the independent variable $x$) from -2 to 2 can be used to obtain output values (the dependent variable $y$) from 5 to 9.  
  • Inconsistent and Dependent Systems in Three Variables

    • Systems of equations in three variables are either independent, dependent, or inconsistent; each case can be established algebraically and represented graphically.
    • There are three possible solution scenarios for systems of three equations in three variables:
    • Independent systems have a single solution.
    • The same is true for dependent systems of equations in three variables.
    • Now, notice that we have a system of equations in two variables:
  • Inconsistent and Dependent Systems in Two Variables

    • An independent system of equations has exactly one solution $(x,y)$.
    • The previous modules have discussed how to find the solution for an independent system of equations.
    • When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set.
    • Systems that are not independent are by definition dependent.
    • A system of equations whose left-hand sides are linearly independent is always consistent.
  • Inconsistent and Dependent Systems

    • ) and dependency (are the equations linearly independent?
    • is a system of three equations in the three variables x, y, z.
    • When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set.
    • For linear equations, logical independence is the same as linear independence.
    • Systems that are not independent are by definition dependent.
  • Introduction to Systems of Equations

    • For example, consider the following system of linear equations in two variables:
    • The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
    • is a system of three equations in the three variables $x, y, z$.
    • Each of these possibilities represents a certain type of system of linear equations in two variables.
    • An independent system has exactly one solution pair $(x, y)$.
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