direction

(noun)

Increasing, decreasing, horizontal or vertical. 

Related Terms

  • steepness
  • slope

Examples of direction in the following topics:

  • Direct Variation

    • When two variables change proportionally, or are directly proportional, to each other, they are said to be in direct variation.
    • When two variables change proportionally to each other, they are said to be in direct variation.
    • Direct variation is easily illustrated using a linear graph.
    • Graph of direct variation with the linear equation y=0.8x.
    • The line y=kx is an example of direct variation between variables x and y.
  • Direct and Inverse Variation

    • Two variables in direct variation have a linear relationship, while variables in inverse variation do not.
    • If $x$ and $y$ are in direct variation, and $x$ is doubled, then $y$ would also be doubled.
    • Direct variation is represented by a linear equation, and can be modeled by graphing a line.
    • Inverse variation is the opposite of direct variation.
    • Relate the concept of slope to the concepts of direct and inverse variation
  • Stretching and Shrinking

    • Stretching and shrinking refer to transformations that alter how compact a function looks in the $x$ or $y$ direction.
    • This leads to a "stretched" appearance in the vertical direction.
    • If the function $f(x)$ is multiplied by a value less than one, all the $y$ values of the equation will decrease, leading to a "shrunken" appearance in the vertical direction.  
    • This leads to a "shrunken" appearance in the horizontal direction.
    • 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.  
  • Introduction to the Polar Coordinate System

    • The first coordinate $r$ is the radius or length of the directed line segment from the pole.
    • The angle $θ$, measured in radians, indicates the direction of $r$. 
    • We move counterclockwise from the polar axis by an angle of $θ$,and measure a directed line segment the length of $r$ in the direction of $θ$. 
    • Adding any number of full turns ($360^{\circ} $ or $2\pi$ radians) to the angular coordinate does not change the corresponding direction.
    • Also, a negative radial coordinate is best interpreted as the corresponding positive distance measured in the opposite direction.
  • Combined Variation

    • Before go deeper into the concept of combined variation, it is important to first understand what direct and inverse variation mean.
    • Simply put, two variables are in direct variation when the same thing that happens to one variable happens to the other.
    • If x and y are in direct variation, and x is doubled, then y would also be doubled.
    • To have variables that are in combined variation, the equation must have variables that are in both direct and inverse variation, as shown in the example below.
    • Apply the techniques learned with direct and inverse variation to combined variation
  • Translations

    • A translation of a function is a shift in one or more directions.
    • A translation moves every point in a function a constant distance in a specified direction.
  • Rules for Solving Inequalities

    • Take note that multiplying or dividing an inequality by a negative number changes the direction of the inequality.
    • Now, multiply the same inequality by -3 (remember to change the direction of the symbol):
    • This statement also holds true, and it demonstrates how crucial it is to change the direction of the greater than or less than symbol.
    • Multiply both sides by -3, remembering to change the direction of the symbol:
  • Slope

    • Slope describes the direction and steepness of a line, and can be calculated given two points on the line.
    • In mathematics, the slope of a line is a number that describes both the direction and the steepness of the line.
    • The direction of a line is either increasing, decreasing, horizontal or vertical.
  • Parts of a Parabola

    • The sign on the coefficient $a$ determines the direction of the parabola.
  • The Cartesian System

    • The arrows on the axes indicate that they extend forever in their respective directions (i.e. infinitely).
    • The arrows on the axes indicate that they extend forever in their respective directions (i.e. infinitely).
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