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# Col Alg for Math,Science,Engin MTH 111C

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This 5 page Class Notes was uploaded by August Feeney on Monday October 19, 2015. The Class Notes belongs to MTH 111C at Portland Community College taught by Staff in Fall. Since its upload, it has received 72 views. For similar materials see /class/224641/mth-111c-portland-community-college in Math at Portland Community College.

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Date Created: 10/19/15

Haberman King MTH lllc Section 1 Sets and Functions Module 4 The Algebra of Functions We can use the four basic arithmetic operations addition subtraction multiplication and division to create new functions from old ones DEFINITION If f and g are functions and x represents a value in both of their domains then we can define the following four functions SumofFunctions f gx f x gx DifferenceofFunctions f gx f x gx ProductofFunctions fgx fx39gx QuotientofFunctions LJOQ fx gx 0 it is important to note that g gx gx 0 since this would cause division by zero and division by zero is undefined EXAMPLE Suppose that the function s ft represents the total number of female students enrolled at PCC t years after 1990 and that s mt represents the total number of male students enrolled at PCC t years after 1990 Write an expression that represents the total number of students enrolled at PCC t years after 1990 SOLUTION s fmt represents the total number of students enrolled at PCC t years after 1990 10 1x239 EXAMPLE Let hx 5 7x and kx a Find and simplify the rule for hkx b Find and simplify the rule for hkx c Evaluate hk2 D Evaluate 1 e Evaluate k h 3 SOLUTIONS hkx hx kx 5 7x 10 2 1x 1x2 10 2 2 1x 1x 5 7x 5 7x1 x2 Jri 1x2 1x2 5 7x1x210 1x2 7x35x2 7x15 1x2 lthkgtxs7x 10 J 1x2 105 7x 1x2 50 70x 1x2 c We can do this one two ways First we ll use the formula we found in a Since 3 2 hkx 7x 5x 27x15 1x we see that Ham 2 723 522 72 15 122 5620 1415 35 T 7 Alternatively we can calculate k2 and k2 separately and then add the results h k2 k2 k2 10 5 7 2 lt ltgtgt My 9 5 92 7 d As with c we can do this two ways Since we haven t yet found a formula for x we ll just calculate h1 and kl and then divide the results h h 1 2 lt1 5 71 10 1 12 2 5 l 5 k h 3 k 3 h 3 L 1 42 5 7 3 ILOQJ 521 1 26 25 EXAMPLE Given the graphs of y fx and y gx in Figures 1 and 2 respectively graph y fgx in Figure 3 Figure 1 Graph of y fx Figure 2 Graph of y gx SOLUTION T0 graph y fgx choose an input value and add the corresponding output values For instance f4 4 and g4 1so fg4 5while fg 6 2 since f 6 1 and g 6 1 Figure 3 Graph of y fgx Try this one yourself and check your answer If 2x71 and gx7x 3find 3 fgx 6 f39gx b figx d SOLUTIONS a Click here for solution b Click here for solution c Click here for solution d 105 2x 31 for x 3 it is important to note that x 3 since this would cause g 7x division by zero and division by zero is undefined Try this one yourself and check your answer Fill in the missing parts of the table below f 00 got g 3 CLICK HERE FOR SOLUTION

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