141.2Function NotationYOU WILL NEED•graphing calculatorUse function notation to represent linear and quadratic functions.GOALLEARN ABOUTthe MathThe deepest mine in the world, East Rand mine in South Africa,reaches 3585 m into Earth’s crust. Another South African mine,Western Deep, is being deepened to 4100 m. Suppose thetemperature at the top of the mine shaft isand that itincreases at a rate ofas you descend.0.015°C>m11°CFunction Notation1.2What is the temperature at the bottom of each mine??EXAMPLE1Representing a situation with a functionand using it to solve a problema)Represent the temperature in a mine shaft with a function. Explain whyyour representation is a function, and write it infunction notation.b)Use your function to determine the temperature at the bottom of East Randand Western Deep mines.Lucy’s Solution: Using an Equationa)An equation for temperature iswhereTrepresents the temperature indegrees Celsius at a depth ofdmetres.The equation represents a function.Temperature is a function ofdepth.In function notation,T(d)51110.015d.T51110.015d,I wrote a linear equation for theproblem.I used the fact thatTstarts atand increases at a steady rate ofSince this equation represents a linearrelationship between temperature anddepth, it is a function.I wrote the equation again.T(d) makesit clearer thatTis a function ofd.0.015 °C>m.11°Cfunction notationnotation, such asf(x), used torepresent the value of thedependent variable—theoutput—for a given value of theindependent variable,x—theinputThe notationsyandareinterchangeable in theequation or graph of afunction, soyis equal toThe notationis read “fatx” or “fofx.” The symbolsandare oftenused to name the outputs offunctions, but other letters arealso used, such asforvelocity as a function of time.v(t)h(x)g(x),f(x),f(x)f(x).f(x)CommunicationTip

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15Chapter 1Introduction to FunctionsI found the temperature at thebottom of East Rand mine bycalculating the temperature at adepth of 3585 m. I substituted3585 fordin the equation.For the new mine, I wanted thetemperature whensoI calculatedT(4100).d54100,b)The temperatures at the bottom of EastRand mine and Western Deep mine areaboutand, respectively.73°C65°C572.5511161.5T(4100)51110.015(4100)564.775511153.775T(3585)51110.015(3585)I wrote an equation to showhow the temperature changesas you go down the mine.I knew that the relationship waslinear because the temperatureincreases at a steady rate. I useddfor depth and called thefunctionT(d)for temperature.I made a table of values for thefunction.I substituted thed-values intothe function equation to gettheT(d)-values.a)This is a function because it is alinear relationship.

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Term

Spring

Professor

Carter

Tags

Quadratic equation, Tim