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1.1. FUNCTIONS AND CHANGE. A function is used to represent the dependence of one quantity upon another. Table of a function. Is there a formula or rule for this function?. input – independent variable output – dependent variable. discrete values : isolated values like a date.

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  1. 1.1 FUNCTIONS AND CHANGE

  2. A functionis used to represent the dependence of one quantity upon another. Table of a function Is there a formula or rule for this function? input – independent variable output – dependent variable discrete values: isolated values like a date continuous values: continuous like time

  3. Graph of a function Chirps per minute of a cricket C related to the temperature T in degrees Fahrenheit. C = 4T - 160 Formula of a function

  4. Example 1: For the function C = f(T) what is the domain and range? Solution: Domain = All T values between 40° F and 136° F = All T values with 40 ≤ T ≤ 136 = [40, 136] Range = All C values from 0 to f(136) = 384 = All C values with 0 ≤ C ≤ 384 = [0, 384]

  5. Consider the linear function y = f(t) = 130 + 2t which represents the Olympics winning pole vault height in inches and t is the number of years since 1900. Since f(t) increases with t, we say that f is an increasingfunction. The coefficient 2 tells us the rate at which the height increases: The formula would predict that the height in the 2012 Olympics would be 29 ft 6 inches but was actually only 19 feet 7 inches.

  6. The linear function y = g(t) = 260 – 0.39t represents the world record to run the mile, in seconds and t is the number of years since 1900. Since g(t) decreases with t, we say that f is an decreasingfunction.

  7. For example, the area of a circle is proportional to the square of the radius, r, because A = f(r) = πr2 . We say one quantity is inversely proportional to another if one is proportional to the reciprocal of the other. ( y = k/x) For example, the speed, v, at which you make a 50-mile trip is inversely proportional to the time, t, taken, because v = 50(1/t) = 50/t.

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