3.6 Start Thinking. 3.6 Warm Up. 3.6 Cumulative Review Warm Up. = 2. ( q )

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1 .6 Start Thinking Graph the lines = and =. Note the change in slope of the line. Graph the line = 0. What is happening to the line? What would the line look like if the slope was changed to 00? 000? What if the slope was the greatest number ou can think of? Eplain how this shows the slope of a vertical line is undefined..6 Warm Up Graph the point and its image in a coordinate plane.. P(, ); reflected in the -ais. Q(, ); reflected in the -ais. R(, ); reflected in the line through (, ) and (, ). S (, ); reflected in the line through (, ) and ( 8, ).6 Cumulative Review Warm Up Solve the equation.. c c =. ( q ). ( g ) = q 0 = 6 g. m + =. 6w 9w = 6. k ( k ) + + = 9 98 Algebra Copright Big Ideas Learning, LLC

2 Name Date.6 Practice A In Eercises and, use the graphs of f and g to describe the transformation from. f() = +. g() = f() g() = f( + ) f() =. You and a friend start running from the same location. Your distance d (in miles) after t minutes is dt () = 7 t. Your friend starts running 0 minutes after ou. Your friend s distance f is given b the function f() t = d( t 0 ). Describe the transformation from the graph of d to the graph of f. In Eercises and, use the graphs of f and h to describe the transformation from the graph of f to the graph of h... 8 f() = + h() = f( ) f() = h() = f() 8 In Eercises 6 and 7, use the graphs of f and r to describe the transformation from the graph of f to the graph of r. 6. f ( ) = + ; r( ) = f( ) 7. f ( ) = + 6; r( ) = f( ) In Eercises 8 and 9, write a function g in terms of f so that the statement is true. 8. The graph of g is a vertical translation units down of the graph of f. 9. The graph of g is a reflection in the -ais of the graph of f. Copright Big Ideas Learning, LLC Algebra 99

3 Name Date.6 Practice B In Eercises and, use the graphs of f and g to describe the transformation from. f( ) = ; g( ) = f( + ). f( ) = ; g( ) = f( 6). The total cost C (in dollars) to rent a -foot b 0-foot canop for d das is given b the function Cd ( ) = d + 0, where the setup fee is $0 and the charge per da is $. The setup fee increases b $0. The new total cost T is given b the function Td ( ) = Cd ( ) + 0. Describe the transformation from the graph of C to the graph of T. In Eercises and, use the graphs of f and h to describe the transformation from the graph of f to the graph of h.. f ( ) = ; h( ) = f( ). f ( ) = + ; h( ) = f( ) In Eercises 6 and 7, use the graphs of f and r to describe the transformation from the graph of f to the graph of r. 6. f ( ) 0; r( ) f ( ) = = 7. f ( ) = + ; r( ) = 6 f( ) In Eercises 8, use the graphs of f and g to describe the transformation from = + = 9. f ( ) = + 6; g( ) = f ( ) 8. f( ) ; g( ) f( ) 0. f ( ) = ; g( ) = f( ). f( ) g( ) f( ) = ; = + In Eercises and, write a function g in terms of f so that the statement is true.. The graph of g is a horizontal shrink b a factor of of the graph of f.. The graph of g is a horizontal translation units left of the graph of f. In Eercises 7, graph f and h. Describe the transformations from the graph of f to the graph of h.. f( ) = ; h( ) = +. ( ) ( ) f = ; h = + 6. f( ) = ; h( ) = 8 7. ( ) ( ) f = ; h = 00 Algebra Copright Big Ideas Learning, LLC

4 Name Date.6 Enrichment and Etension Multiple Transformations of Linear Equations Eample: Let f( ) =. Graph the transformation g ( ) f( ) Use composition of functions to rewrite g( ). Then find g(, ) g( 0, ) and g( ) check our graph. f() = ( ) ( ( ) ) ( ) = ( ) + ( ) = g g g = + = +. to g ( ) ( ) () = 8 g 0 = g = 0 g() = f( ) + Let f( ). rewrite ( ). = + Graph each transformation given. Use composition of functions to g Then find g( ) g( ) g( ), 0, and. g = f. ( ). g ( ) = f( + ) +. g ( ) f( ) = What is different about Eercise? Is it possible to write a rule for this tpe of transformation? If so, please demonstrate. Copright Big Ideas Learning, LLC Algebra 0

5 Name Date.6 Puzzle Time What Did One Watch Sa To The Other Watch? Write the letter of each answer in the bo containing the eercise number. Describe the transformations from the graph of f to the graph of g.. f( ) = 7; g( ) = f( ). f ( ) = + 9; g( ) = f( ) f = g = f. ( ) 6 ; ( ) = 8; =. f( ) g( ) f( ). f ( ) = 0 + ; g( ) = 8 f ( ) f = ; g = ( ) ( ) 9 f = g = ( ) ; ( ) f = ; g = 6 8. ( ) ( ) f = ; g = 9. ( ) ( ) 0. Members of the marching band need to rent a moving van to haul their instruments back and forth to several competitions. The total cost C (in dollars) to rent a moving van for m miles is given b the function Cm ( ) = m +, where the flat fee is $ and the charge per mile is $. The flat fee decreases b $. The new total cost T is given b the function Tm ( ) = Cm ( ). Describe the transformation from the graph of C to the graph of T. Answers G. vertical stretch b a factor of 8 I. reflection in the -ais and a vertical translation 9 units up 6 A. reflection in the -ais T. horizontal stretch b a factor of and a vertical translation 6 units down N. vertical translation units down U. vertical translation units down E. horizontal translation units right M. horizontal shrink b a factor of and a vertical translation units down T. vertical translation 6 units up O. horizontal stretch b a factor of Algebra Copright Big Ideas Learning, LLC