3.7 Start Thinking. 3.7 Warm Up. 3.7 Cumulative Review Warm Up

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1 .7 Start Thinking Use a graphing calculator to graph the function f ( ) =. Sketch the graph on a coordinate plane. Describe the graph of the function. Now graph the functions g ( ) 5, and h ( ) 5 the same coordinate plane. Eplain wh the graphs of g ( ) and h ( ) are not the same. = + = + on.7 Warm Up Solve the equation, if possible.. n 8 =. b 5 =. z + = 0. t + 5 = n = 5. h = 7 7. n + = 8. 5t + 7 =.7 Cumulative Review Warm Up Write the sentence as an inequalit. Then solve the inequalit.. A number minus 7 is less than.. A number plus is at most.. The sum of a number and 8 is greater than 5.. The number 5 is greater than or equal to the difference of a number and. 0

2 Name Date.7 Practice A In Eercises, graph the function. Compare the graph to the graph of f = Describe the domain and range. ( ).. g ( ) =. p ( ) = +. h ( ) = + 5. k ( ) = In Eercises 5 and, graph the function. Compare the graph to the graph of f = + ( ). 5. h ( ) = +. h ( ) = + In Eercises 7 and 8, compare the graphs. Find the value of h, k, or a g() = + k f() = f() = h() = h In Eercises 9 and 0, write an equation for h() that represents the given g = 9. vertical translation units up 0. vertical stretch b a factor of In Eercises and, graph and compare the two functions. f = ; g =. ( ) ( ) m = + 5; n = + 5. ( ) ( ). The number of ice cream cones sold c (in hundreds) increases and then decreases as described b the function ct () = 5 t + 0, where t is the time (in months). a. Graph the function. b. What is the greatest number of ice cream cones sold in month? 0 Algebra Copright Big Ideas Learning, LLC

3 Name Date.7 Practice B In Eercises, graph the function. Compare the graph to the graph of f = Describe the domain and range. ( ).. m ( ) =. t ( ) =. g( ) =. z ( ) = In Eercises 5 and, graph the function. Compare the graph to the graph of f = + ( ). 5. k ( ) = 5 +. q ( ) = In Eercises 7 and 8, compare the graphs. Find the value of h, k, or a f() = f() = s() = a w() = a In Eercises 9 and 0, write an equation for h() that represents the given g = 9. horizontal translation 7 units right 0. vertical shrink b a factor of and a reflection in the -ais In Eercises and, graph and compare the two functions. c = + ; d = +. ( ) ( ) p = + ; q = + 5. ( ) ( ). Graph = + 5 and = 8 in the same coordinate plane. Use the graph to solve the equation + 5 = 8. Check our solutions. 05

4 Name Date.7 Enrichment and Etension Transformations and Compositions Eample: Graph = +, and then state the domain and range in interval notation. First graph the function on the inside of the outer absolute value. Then invert all the negative -values to positive -values, because the final output of this particular absolute value function must be all positive numbers. domain: (, ) range: [ 0, ) In Eercises, graph each function and state the domain and range in interval notation.. =. =. = +. = 5. =. = 0 Algebra Copright Big Ideas Learning, LLC

5 Name Date.7 Puzzle Time What Do Sharks Eat For Dinner? 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 = ; g = +. ( ) ( ) f = ; g =. ( ) ( ). ( ) ; ( ) f = g = f = g =. ( ) ; ( ) f = 7; g = 7 5. ( ) ( ) f = + ; g = + 8. ( ) ( ) f = + 9 ; g = ( ) ( ) f = + 8; g = ( ) ( ) Write an equation that represents the given f = 9. horizontal translation units left and a reflection in the -ais 0. vertical stretch b a factor of and a reflection in the -ais. a reflection in the -ais and a vertical translation units up. horizontal shrink b a factor of and a vertical Answers I. g ( ) = + P. reflection in the -ais F. horizontal translation units right and vertical translation 8 units up N. reflection in the -ais and a vertical stretch b a factor of D. vertical shrink b a factor of H. horizontal translation units right and vertical translation units down A. vertical translation units up H. g ( ) = + C. g( ) = I. g ( ) = S. horizontal translation units right S. horizontal shrink b a factor of translation units down