CA_GPS_3 - f may be expressed as b ax x f = a 2 3 = x x f b 2 2 = x x f c x x x f 3 2 4 3 8 = d 4 = x x f 2 a Find the slope if it exists of the

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Rev. S08 http://faculty.valenciacc.edu/ashaw/ COLLEGE ALGEBRA NAME: ________________________________ GPS # 3 1.3 LINEAR FUNCTIONS Class Time: ____________ Date: __________ Useful Guidelines: * Linear Function: b ax x f + = ) ( [If b x f = ) ( (constant function) and if x x f = ) ( (Identity Function)] Its graph is a straight line. For each unit increase in x , ) ( x f changes by an amount equal to a . * Rate of Change for a Linear Function ( slope of the graph ): The output of a linear function changes by a constant amount for each unit increase in the input. * When data have a constant rate of change , they can be modeled by b ax x f + = ) ( . The constant a represents the rate of change , and the constant b represents the initial amount or the value when 0 = x . * The slope of a line through the points 1 1 ( , ) x y and 2 2 ( , ) x y is 2 1 2 1 y y rise m x x run ! = = ! 1 2 ( ) x x ! . “Slope Formula” 1. Determine whether f is a linear function. If f is linear, give values for a and b so that
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Unformatted text preview: f may be expressed as b ax x f + = ) ( . a) 2 3 ) ( ! ! = x x f b) 2 ) ( 2 ! = x x f c) x x x f 3 2 4 3 8 ) ( + ! = d) 4 ) ( + = x x f 2. a) Find the slope, if it exists, of the line passing through the points (1,9) and (8,18) . b) If a linear function has the points (1,9) and (8,18) on its graph, what is the rate of change of the function? 3. Use the intercepts to graph the following equations. a) 2 4 y x ! = ! b) 3 9 x y + = 4. Suppose the monthly cost for the manufacture of tennis balls is x x C 21 . 1220 ) ( + = , where x is the number of tennis balls produced each month. a) What is the slope of the graph of the total cost function? b) What is the marginal cost (rate of change of the cost function) for the product? c) What is the cost of each additional ball that is produced in a month?...
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This note was uploaded on 10/18/2011 for the course MAC 1105 taught by Professor Russel during the Summer '07 term at Valencia.

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