C Challenge

44. Reasoning Find a sequence of basic transformations by which the polynomial function y = 2 x 3 − 6 x 2 + 6 x + 5 y equals 2 , x cubed , minus , 6 x squared , plus 6 x plus 5  can be derived from the cubic function y = x 3 . y equals , x cubed , .
45. Physics For a constant resistance R (in ohms), the power P (in watts) dissipated across two terminals of a battery varies directly as the square of the current I (in amps). If a battery connected in a circuit dissipates 24 watts of power for 2 amps of current flow, how much power would be dissipated when the current flow is 5 amps?
46. Writing Give an argument that shows that every polynomial family of degree n > 2 n greater than 2  contains polynomials that cannot be generated from the basic function y = x n y equals , x to the n  by using stretches, compressions, reflections, and translations.

Standardized Test Prep

Use the graph to answer questions 47–49.

SAT/ACT

47. Which equation does the graph represent?

    1. y = ( x + 2 ) 2 − 1 y equals open x plus 2 , close squared , minus 1
    2. y = ( x − 2 ) 2 − 1 y equals . open x minus 2 close squared . minus 1
    3. y = ( x − 2 ) 2 − 1 y equals . open x minus 2 close squared . minus 1
    4. y = ( x − 2 ) 4 − 1 y equals . open x minus 2 close to the fourth . minus 1

48. If y = f ( x ) y equals f open x close  is an equation for the graph, what are factors of f ( x ) ? f open x close question mark

    

    6. ( x − 1 )  and  ( x + 3 ) open x minus 1 close , and , open x plus 3 close
    7. ( x − 1 )  and  ( x − 3 ) open x minus 1 close , and , open x minus 3 close
    8. ( x + 1 )  and  ( x − 3 ) open x plus 1 close , and , open x minus 3 close
    9. ( x + 1 )  and  ( x + 3 ) open x plus 1 close , and , open x plus 3 close

Short Response

49. If y = a x 2 + b x + c y equals eh , x squared , plus b x plus c  is an equation for the graph, what type of number is its discriminant?

Mixed Review

See Lesson 5-8.

Find a polynomial function whose graph passes through the given points.

50. ( − 1 , 4 ) , ( 0 , − 2 ) , ( 1 , − 2 ) , ( 2 , − 8 ) open negative 1 comma 4 close comma open 0 comma negative 2 close comma open 1 comma negative 2 close comma open 2 comma negative 8 close
51. ( − 2 , − 17 ) , ( 0 , − 3 ) , ( 1 , − 5 ) , ( 3 , 63 ) open negative 2 comma negative 17 close comma open 0 comma negative 3 close comma open 1 comma negative 5 close comma open 3 comma 63 close

See Lesson 2-4.

Write an equation of each line.

52. slope  = − 4 5 ; slope , equals negative , 4 fifths . semicolon  through ( − 1 , 4 ) open negative 1 comma 4 close
53. slope  = − 3 ; slope , equals negative 3 semicolon  through ( 2 , − 1 ) open 2 comma negative 1 close

See Lesson 2-1.

Determine whether each relation is a function.

54. { ( 0 , − 1 ) , ( − 1 , 3 ) , ( 2 , 3 ) , ( − 3 , 3 ) } the set open 0 comma negative 1 close comma open negative 1 comma 3 close comma open 2 comma 3 close comma open negative 3 comma 3 close end set
55. { ( − 4 , 0 ) , ( − 7 , 0 ) , ( − 4 , 1 ) , ( − 7 , 1 ) } the set open negative 4 comma 0 close comma open negative 7 comma 0 close comma open negative 4 comma 1 close comma open negative 7 comma 1 close end set

Get Ready! To prepare for Lesson 6-1, do Exercises 56–58.

See Lesson 5-2.

Factor each expression.

56. x 10 + x 2 x to the tenth , plus , x squared
57. x 4 − y 4 x to the fourth , minus , y to the fourth
58. 169 x 6 y 12 − 13 x 3 y 6 169 , x to the sixth , y to the twelfth , minus , 13 x cubed . y to the sixth

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