185 Holt McDougal Algebra 1

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1 61. = - 1 (, = 1 = (, 1 = 1 1 = (1, 0 = 0 1 = 1 (0, 1 1 = 1 1 = 0 (1, 0 = 1 = 1 (, 1 = 1 = (, 4 = 4 1 = (4, Draw a line through all the points to show all ordered pairs that satisf the function. Draw arrowheads on both ends of the line. 6. = - (, = ( = 6 (, 6 = ( = 1 (, 1 1 = (1 = (1, 0 = (0 = (0, 1 = (1 = (1, = ( = 1 (, 1 = ( = 6 (, = m( 1 (1 = _ ( = _ ( = _ = _ 6. 1 = m( 1 0 = ( (1 = ( + 1 = = m( 1 = 0 ( ( = 0( + = = Draw a smooth curve through all the points to show all ordered pairs that satisf the function. Draw arrowheads on both ends of the curve = m( 1 4 = ( 4 = = = m( 1 7 = ( 7 = = = m( 1 ( = ( (4 + = ( = + 4 = 6_ -9 TRANSFORMING LINEAR FUNCTIONS, PAGES 697 CHECK IT OUT! 1. The graph of g( = is the result of translating the graph of f( = + 4, 6 units. The graph of g( = 1 is the result of rotating the graph of f( = 1 about (0, 1. The graph of g( is less steep than the graph of f(.. To find g(, multipl the value of m b 1. In f( = _ +, m = _. _ (1 = _ g( = _ + 4. Multipl f( b 1 to get h( =. This reflects the graph across the -ais. Then add to h( to get g( = +. This translates the graph units up.. If the charge per letter is lowered to $0.1, the new function is g( = The original graph will be rotated about (0, 17 and become less steep. If the troph s cost is raised to $180, the new function is h( = The original graph will be translated units up. THINK AND DISCUSS 1. translation of f( =.4 units up. No; there can onl be a whole number of letters, so points whose -coordinates are not whole numbers have no meaning in this situation. 18 Holt McDougal Algebra 1

2 . EXERCISES GUIDED PRACTICE 1. translation. rotation The graph of g( = 4 is the result of translating the graph of f( =, 4 units The graph of g( = + 1 is the result of translating the graph of f( =, 1 units up. The graph of g( = + is the result of translating the graph of f( =, units up. The graph of g( = 6. is the result of translating the graph of f( =, 6. units The graph of g( = is the 4 result of rotating the graph of f( = about (0, 0. The graph of g( is less steep than the graph of f( The graph of g( = + is the result of rotating the graph of f( = + about (0,. The graph of g( is steeper than the graph of f(. The graph of g( = 4 is the result of rotating the graph of f( = about (0,. The graph of g( is steeper than the graph of f(. The graph of g( = + 1 is the result of rotating the graph of f( = + 1 about (0, 1. The graph of g( is less steep than the graph of f(. To find g(, multipl the value of m b 1., m = In f( = (1 = g( =. To find g(, multipl the value of m b 1. In f( = + 4, m =. (1 = g( = + 4 To find g(, multipl the value of m b 1. In f( = 6, m =. (1 = g( = 6 To find g(, multipl the value of m b 1. In f( = 1, m =. (1 = g( = Holt McDougal Algebra 1

3 g f g f f g Multipl f( b to get h(. This makes it steeper. Then subtract from h( to get g(. This translates the graph units Multipl f( b to get h( _. This rotates the graph and makes it less steep. Then add 1 to h( to _ get g( + 1. This translates the graph 1 units up. Add 1 to f( to get h(. This translates the graph 1 unit up. Then multipl h( b 4 to get g( 4. This reflects the graph in the -ais and makes it steeper.. f. f 4. g f g g The graph of g( 10 1 is the result of rotating the graph of f( 1 about (0, 1. The graph of g( is less steep than the graph of f(. The graph of g( _ + is the result of rotating the graph of f( + about (0,. The graph of g( is less steep than the graph of f(. To find g(, multipl the value of m b 1. In f( 6, m 6. 6( 1 6 g( f g Multipl f( b to get h( _. This rotates the graph about (0, 0 and makes it less steep. Then subtract from h( to get g(. This translates the graph units 19. If the reservation fee is raised to $0, the new function is g( The original graph will be translated units up. If the charge per person is lowered to $1, the new function is h( 1 +. The original graph is rotated about (0, and becomes less steep. PRACTICE AND PROBLEM SOLVING 0. The graph of g( + is f the result of translating the graph of f(, unit up.. f 6. g 7. g f g f To find g(, multipl the value of m b 1. In f(, m ( 1 g( Multipl f( b to get h( 4. This makes the graph steeper. Then subtract 1 from h( to get g( 4 1. This translates the graph 1 unit Subtract from f( to get h( 7. This translates the graph units Then multipl h( b to get g( 14. This makes the graph steeper. g 1. f g The graph of g( 4 is the result of translating the graph of f(, 4 units 8. If the number of parents is reduced to 0, the new function is g(. The original graph will be 4 translated units If the number of teachers is raised to 1 for ever students, the new function is h( +. The original graph will be rotated about (0, and become steeper. 187 Holt McDougal Algebra 1

4 9. The graph of g( is the result of reflecting the graph of f( across the -ais. The graphs have oppposite slopes same steepness but f opposite in directions. The graphs have the same -intercept. g. Possible answer: 6. g( 0. The graph of g( + 8 is the result of translating the graph of f( 8 units up. g The graphs have the same slope but different -intercepts. g( + Answers ma var depending on the point of rotation used. 7. g( 6 4 f 1. The graph of g( is the result of rotating the graph of f( about (0, 0 The graph of g( is steeper than the graph of f(. The graphs have different slopes but the same -intercept. f g _. The graph of g( is the result of rotating the 7 graph of f( about (0, 0. The graph of g( is less steep than the graph of f(. The graphs have different slopes but the same -intercept. f 8a " OOK#LUB #OSTS #OSTS " OOKSPURCHASED b " OOK#LUB #OSTS g #OSTS. 4. g f Multipl f( b 6 to get h( 6. This rotates the graph about (0, 0 and makes it steeper. Then subtract from h( to get g( 6. This translates the graph units The graphs have different slopes and different intercepts, but both graphs are increasing. Multipl f( b to get h(. This rotates the f graph about (0, 0 and makes it steeper. Then add 1 to h( to get g( + 1. This translates g the graph 1 unit up. The graphs have different slopes and different intercepts. " OOKSPURCHASED c. The graph in part a is translated 10 units up to get the graph in part b. 9. trans. 9 units down 40. rot. about (0, 0; ref. across -ais 41. rot. about (0, 0 (steeper 4. rot. about (0, 0 (less steep, and trans. 1 unit up 4. rot. about (0, 0 (steeper 44. rot. about (0, 0 (less steep 4a. $00 b % c. Commisson changes to %; base pa changes to $ Possible answer: reflect across the -ais 188 Holt McDougal Algebra 1

5 47. Possible answer: A reflection across the -ais multiplies the -coordinate of each ordered pair b 1. For eample, when f( is reflected across the -ais, the coordinate changes to. (i.e., (1, 0 ( 1, 0 48a. b. Possible answer: Jen is walking from the stadium to the softball field, and the stadium is 100 ft closer to the field than the school is. c. The distance from the school when the walking begins. TEST PREP 49. D; If the slope changes to 10, the new function is g( 10. The -intercept can be found b substituting 0 for g( which gives 0 10 or. 0. J; Since the slope will not change b increasing the -intercept, the new line is not steeper than the original. CHALLENGE AND EXTEND 1. The graph of g( + is the result of translating the graph of f(, units to the left.. The graph of g( + c is the result of translating the graph of f(, c units to the left. The graph of g( c is the result of translating the graph of f(, c units to the right. SPIRAL REVIEW. P P + w ( + ( ( + ( Positive correlation; as it gets hotter, more people bu ice cream. 6. Positive correaltion; as ou use more electricit, our electricit bill increases. 7. Negative correaltion; as ou drive farther, the amount of gasoline in the tank decreases ( The lines decribed b + and 4 represent parallel lines. The each have slope ( The lines described b + 1 each have slope and ( represent parallel lines. The. 1 1 _ _ 7 The slope of the line decribed b is. The slope of the line described b + 1 is _. ( _ 1 These lines are perpendicular because the product of their slopes is 1. The slope of the line described b 1 is _. The slope of the line described b _ is _. _ ( _ 1 These lines are perpendicular because the product of their slopes is Holt McDougal Algebra 1

6 ( 1( The line described b 4 is a vertical line and the line described b is a horizontal line. These lines are perpendicular. The slope of the line described b + 6 is. The slope of the line described b + is. ( 1 These lines are perpendicular because the product of their slopes is _ 6 _ Plot (0, 1. Count 1 unit up and units right and plot another Plot (0, 4. Count 0 units up and 1 unit right and plot another point. Draw the line connecting the two points. READY TO GO ON? PAGE Plot (0,. Count 1 unit up and 4 units right and plot another point. Draw the line connecting the two points. Plot (0,. Count units down. Plot (0, 6. Count 1 unit down Plot (0,. Count units down the two. 7a b. The -intercept is. This is the entrance fee. The slope is 0.. This is the cost per bowl of chili m _ 1 1 Plot (0,. Count units down Plot (,. Count units down and units right and plot another Plot (, 1. Count units up _ m( 1 1 ( m _ 1 _ 7 ( ( 1 1 m( 1 7 4( _ 1 8_ Holt McDougal Algebra 1

SLOPE A MEASURE OF STEEPNESS through 7.1.5

SLOPE A MEASURE OF STEEPNESS through 7.1.5 SLOPE A MEASURE OF STEEPNESS 7.1. through 7.1.5 Students have used the equation = m + b throughout this course to graph lines and describe patterns. When the equation is written in -form, the m is the