decreasing 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**.