mac1105_lecture14a_1

mac1105_lecture14a_1 - L14a Linear Functions and Models;...

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141 L14a Linear Functions and Models; Quadratic Functions and Models Linear Functions A linear function is a function of the form ( ) fx m x b = + Note: The graph of a linear function is a line with the slope m and the y-intercept b . The domain of a linear function is the set of all real numbers. Example: Graph the function ( ) 24 x = −+ .
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142 Identifying Linear Functions by Using Average Rate of Change The average rate of change y x of a linear function () fx m x b =+ is constant and equal to the slope m . Proof: Important Note : A function ( ) is linear if and only if the average rate of change is constant. Example : Find the average rate of change y x of 2 3 9 x =− from 1 x to 2 x 12 x x .
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143 Example : A manufacturer has been selling 1000 television sets a week at $450 each. A market survey indicates that for each $10 rebate offered to the buyer, the number of sets sold will increase by 100 per week. Determine whether the relation between the price p and demand x is linear and, if so, express p as a linear function of the demand x .
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144 Increasing, Decreasing, and Constant Linear Functions Theorem : The linear function ( ) fx m x b = + over its
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This note was uploaded on 11/07/2011 for the course MAC 1105 taught by Professor Picklesimer during the Fall '10 term at University of Florida.

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mac1105_lecture14a_1 - L14a Linear Functions and Models;...

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