Variation - MAC1105: Variation Consider the two functions 3...

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Unformatted text preview: MAC1105: Variation Consider the two functions 3 f(x) 2x = and 3 3 2 g(x) 2x x- = = = = = = = = . These are both examples of power functions (sec. 4.8 in your text). Power functions have the form n y kx = , where k is called the constant of proportionality and n is a fixed power. Both f and g have a k value of 2 . For f we have n 3 = and for g we have n 3 = - = - = - = - . 1) n > : Consider 3 y 2x = . As input x gets bigger, so does output y . As input x gets smaller, so does output y . This type of relationship between an input and output is called direct variation . We say that y is directly proportional to x . This type of behavior means the graph is increasing . 2) n < : Consider 3 2 y x = . As input x gets bigger, output y gets smaller. As input x gets smaller, output y gets bigger. This type of relationship between an input and output is called inverse variation . We say that y is inversely proportional to x . This type of behavior means the graph is decreasing ....
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