decreasing function

(noun)

Any function of a real variable whose value decreases (or is constant) as the variable increases.

Related Terms

  • constant function
  • increasing function
  • composite function

Examples of decreasing function in the following topics:

  • Increasing, Decreasing, and Constant Functions

    • Functions can either be constant, increasing as $x$ increases, or decreasing as $x $ increases.
    • Similarly, a function is decreasing on an interval if the function values decrease as the input values increase over that interval.
    • The figure below shows examples of increasing and decreasing intervals on a function.
    • The function is decreasing on on the interval: $ (−2, 2)$.  
    • Identify whether a function is increasing, decreasing, constant, or none of these
  • What is a Quadratic Function?

    • A quadratic function is of the general form:
    • A quadratic equation is a specific case of a quadratic function, with the function set equal to zero:
    • Linear functions either always decrease (if they have negative slope) or always increase (if they have positive slope).
    • All quadratic functions both increase and decrease.
    • The slope of a quadratic function, unlike the slope of a linear function, is constantly changing.
  • The Firm in Pure Competition

    • DM and SM represent the market demand and supply functions.
    • Marginal revenue decreases at twice the rate (has twice the slope of the AR) as a linear AR function.
    • Since the slope the AR for the purely competitive firm is 0, the MR does not decrease and lies along the demand and AR functions.
    • (As shown in Panel B.VII.3. ) Note that a decrease in market supply will shift the firm's demand function up.
    • An increase (decrease) in market demand would shift the firm's demand up (down).
  • Aging and the Urinary System

    • As kidneys age, the number of filtering units and nephrons decreases, slowing down kidney function.
    • As with other organs, kidney function may be slightly reduced with aging.
    • The number of filtering units (nephrons) decreases.
    • The overall amount of kidney tissue also decreases.
    • Under usual conditions, kidney function remains normal in an aging person, although sometimes kidneys in an aging person may function more slowly than those of a younger person.
  • Functional Structure

    • An organization with a functional structure is divided based on functional areas, such as IT, finance, or marketing.
    • Functional departments arguably permit greater operational efficiency because employees with shared skills and knowledge are grouped together by functions performed.
    • A disadvantage of this structure is that the different functional groups may not communicate with one another, potentially decreasing flexibility and innovation.
    • Functional structures may also be susceptible to tunnel vision, with each function perceiving the organization only from within the frame of its own operation.
    • Each different functions (e.g., HR, finance, marketing) is managed from the top down via functional heads (the CFO, the CIO, various VPs, etc.).
  • The Supply and Demand for Bonds

    • A decrease in expected inflation increases the bond's demand function shifting rightward.
    • A decrease in the risk of bonds increases the bond's demand function shifting rightward.
    • A decrease in information costs increases the bond's demand function shifting rightward.
    • A decrease in business taxes increases the bond's supply function shifting rightward.
    • For example, a drop in expected inflation causes the supply function to decrease and shift leftward.
  • Exponential Decay

    • Just as a variable can increase exponentially as a function of another, it is possible for a variable to decrease exponentially as well.
    • Just as it is possible for a variable to grow exponentially as a function of another, so can the a variable decrease exponentially.
    • Consider the decrease of a population that occurs at a rate proportional to its value.
    • This rate at which the population is decreasing remains constant but as the population is continually decreasing the overall decline becomes less and less steep.
    • After $15$ years there will be $12.5$, the amount by which the substance decreases is itself slowly decreasing.
  • Graphical Representations of Production and Cost Relationships

    • The short-run, total product function and the price of the variable input(s) determine the variable cost (VC or TVC) function.
    • In Figure V.3, the short-run TP function and VC function are shown.
    • The MC will be decreasing in this range.
    • In the range from LA to LB amount of labour the output rises from QA to QB, TP increases at a decreasing rate (MP will be decreasing in this range.).
    • At the maximum of TP (LB amount of labour, output QB) at point B, the VC function will "turn back" and as output decreases the VC will continue to rise.
  • Stretching and Shrinking

    • 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.  
    • If $b$ is greater than one the function will undergo vertical stretching, and if $b$ is less than one the function will undergo vertical shrinking.
    • If we want to vertically stretch the function by a factor of three, then the new function becomes:
    • 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.  
    • If $c$ is greater than one the function will undergo horizontal shrinking, and if $c$ is less than one the function will undergo horizontal stretching.
  • Demand Function

    • A decrease in demand is a shift to the left.
    • A decrease in income will decrease (shift the demand to the left) demand.
    • An increase in the income will decrease demand while a decrease in income will increase demand.
    • A decrease in PY will increase the quantity demanded for good Y.
    • The demand for X in Panel A decreases for DX to DX**.
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