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FUNCTIONS AND CHANGE

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A function is used to represent the dependence of one quantity upon another.

Is there a formula or rule for this function?

input – independent variableoutput – dependent variable

discrete values: isolated values like a date

continuous values: continuous like time

Table of a function

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Graph of a function

Formula of a functionChirps per minute of a cricket C related tothe temperature T in degrees Fahrenheit.

C = 4T - 160

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Example 1: For the function C = f(T) what is the domain and range?

Range = All C values from 0 to f(136) = 384 = All C values with 0 ≤ C ≤ 384 = [0, 384]

Solution: Domain = All T values between 40° F and 136° F = All T values with 40 ≤ T ≤ 136 = [40, 136]

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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 increasing function.

The coefficient 2 tells us the rate at which the height increases:

The formula would predict that the height inthe 2012 Olympics would be 29 ft 6 inches but was actually only 19 feet 7 inches.

146 138 82 /

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Rise ySlope inches year

Run x

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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 decreasing function.

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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 tothe 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.