Final Jeopardy! Appendix Ch. 1 Ch. 2 Ch. 3 Ch. 4 Ch. 5

Transcription

1 Final Jeopardy! Appendix Ch. 1 Ch. Ch. 3 Ch. 4 Ch

2 APPENDIX 00 Is the triangle with side lengths 17, 15, and 8 a right triangle? Why/Why not?

3 Appendix 00 If a right triangle, the Pythagorean theorem should hold: c = a + b 17 = = = 89 Yes it is a right triangle

4 APPENDIX 400 Find the quotient and remainder 4 (1 x + x ) ( x + x + 1)

5 Appendix 400 ( x x + x + x + 1) 4 (1 ) x x x+ 1 + x+ 1 x + 0x x + 0x x ( x + x + x + x x x 0 x x x x = + x x + 1) x + x+ 1 + x x (1 ) = x x+ 1

6 APPENDIX 600 Solve for x 4( x ) = x 3 x xx ( 3)

7 Appendix 600 4( x ) = x 0,3 x 3 x xx ( 3) x 4( x ) x = x x 3 x 3 x xx ( 3) 4 x( x ) + 3( x 3) = 3 4x x 8x+ 3x 9= 3 x = x ± 4(4)( 6) ± ± = = = =, (4) 8 8 4

8 APPENDIX 800 Two cars enter the Florida Turnpike at Commercial Boulevard at 8:00 A.M., each heading for Wildwood. One car s average speed is 10 miles per hour more than the other s. The faster car arrives at Wildwood at 11:00 A.M., a half an hour before the other car. What was the average speed of each car? How far did each travel?

9 Appendix 800 d v = d = vt t d = d vt 1 = 11 ( v + 10)(3) = v (3.5) 3v + 30 = 3.5v 0.5v = 30 vt v = 60 mph, v = 70mph 1 d = vt d = (70)(3) = 10mi

10 APPENDIX 1000 Rationalize and simplify: 1 1 ( ) ( ) 4 5 xy x y ( xy) 4

11 Appendix ( ) ( ) 4 5 xy x y ( xy) 1 1 ( ) 4 ( ) xy x y = ( xy) 1 1 ( ) xy ( x y ) + + = ( xy) x y xy = x y = x y x y = x y 14

12 CHAPTER 1 00 Find the distance between (-4,) and (4,8) Section 1.1

13 Chapter 1 00 d = x x + y y ( ) ( ) 1 1 d = 4 ( 4) + 8 ( ) ( ) d = 100 = 10

14 CHAPTER Find the Midpoint of the line connecting(-4,) and (4,8) Section 1.1

15 Chapter M M M x + x y + y, 1 1 = 4 + ( 4) 8+ =, = (0,5)

16 CHAPTER Find any intercepts and axes of symmetry y = x + 4 Section 1.

17 Chapter Intercepts: 0= x + 4 x = 4 ( 4, 0) y = 0+ 4 y =± (0, ) & (0, ) Axis of symmetry: x : y = x+ ( ) 4 y y: y y = x+ 4 Yes, symmetric about x axis = ( x) + 4 = x+ 4 No, not symmetric about x axis, hence not symmetric about origin

18 CHAPTER With the given point and slope, find the equation of the line in slope-intercept form. P = (, 4), m= 3 4 Section 1.3

19 Chapter P= (, 4) = ( x, y ); m= 1 1 y y= mx ( x) y 4 = ( x ) y = x

20 CHAPTER Find the standard form of the equation of a circle with endpoints of a diameter at (4,3) and (0,1). Section 1.4

21 Chapter ( ) + ( ) diameter = d = x x y y = 1 1 d 0 radius = r = = x + x y + y center = h k = M = = 1 1 (, ), (, ) 0 then the standard form of a circle is: ( x h) ( x ) ( y ) + = ( x + + ( y k) = r ) ( ) 5 y = 0

22 CHAPTER 00 If 1 3x f( x) =, gx ( ) = x+ x+ 3 Find the domain of f(x)*g(x) Section.1

23 Chapter x f( x) =, gx ( ) = x+ x+ 3 3x f( x)* gx ( ) = ( x+ )( x+ 3) f( x)* gx ( ):{ x x, x, 3}

24 CHAPTER 400 Determine if the function is even, odd, or neither algebraically. 3 y = x 5x + Section.3

25 Chapter x To determine algebraically, substitute (-x) in for x: x y x 3 3 ( ) 5( ) 100-x 5x + y = x x + y = x 5x 3 = + x As some signs change, but not all, we cannot conclude that it is even or odd. (Even=no signs change, Odd=all signs change) Hence it is neither.

26 CHAPTER 600 Locate all intercepts and graph the piecewise function 3 x for x 1 f ( x) = x for 1< x 1 x for 1< x < 9 Section.4

27 Only intercept in the intervals is (0,0). Chapter 600

28 CHAPTER 800 List the transformation and graph each transformation, beginning with the standard graph f( x) = 3 x+ 1 8 Section.4

29 Chapter 800 f( x) = 3 x+ 1 8 Shift one unit left Shift eight units down Compress by a factor of 3

30 CHAPTER 1000 An equilateral triangle is inscribed in a circle of radius r. Express the area within the circle, but outside the triangle as a function of the length of the triangle side, x and r Section.5

31 Chapter 1000 A circle = π r 3 Atriangle = x 4 (divide the equilateral triangle in half; 3 base = x /, hypotenuse=x, find height= x) 3 A= Acircle Atriangle = π r x 4

32 CHAPTER 3 00 The monthly cost C, in dollars, for international calls on a certain cellular phone plan is given by the function Cx ( ) = 0.38x+ 5 Where x is the number of minutes used. (a) What is the cost if you talk on the phone for 50 minutes? (b) Suppose that you budgeted yourself $60 per month for the phone. What is the maximum number of (whole) minutes that you can talk? Section 3.1

33 Chapter 3 00 Cx ( ) = 0.38x+ 5 a) C(50) = 4 b) 60 = 0.38x + 5 x = 144min

34 CHAPTER Determine the slope, y-intercept, where the function is increasing and decreasing and graph the function: 4y+ 10 = 5x Section 3.1

35 Chapter y+ 10 = 5x 4y = 5x 1 y = 13x 3 0 = 13x x =, y = 0 3 y = 3 (0, 3) Increasing on whole real line

36 CHAPTER Graph the function by starting with a basic parabola and use transformations. Find all intercepts and axis of symmetry. Write in y= ax ( h) + k if necessary: Section 3.3 f x x x ( ) =

37 Chapter f( x) = 3x 4x + 45 f x = x x+ = x x+ ( ) 3( 8 15) 3( ) f x = x ( ) 3( 4) 3 Intercepts: = x 0 3( 4) 3 ± 1= x 4 x = 5,3 (3,0) & (5,0) y = 3(0 4) 3 y = 45 (0, 45) Axis of Symmetry: b 4 x = = = 4 a 6

38 CHAPTER A special window has the shape of a rectangle surmounted by an equilateral triangle. If the perimeter of the window is 16 feet, what dimensions will admit the most light? A eq. triangle = 3 4 s x x x Section 3.4 y y x

39 Chapter P= 3x+ y = 16 3 y = 8 x 3 A = xy + x A= 8x+ x 8 4 = x+ x 4 Maximum obtained at vertex of parabola: b 8 16 x = = = 3.7 ft a y.5 ft 3 total height = y + x 5.7 ft

40 CHAPTER Solve the inequality 5x + 16 < 40x Section 3.5

41 Chapter x x x + 16 < 40x x+ < 8 16 x+ < x < x < 0, x > x<, x> x= we can conclude that the graph is nonnegative meaning there are no values less than 0

42 CHAPTER 4 00 Find the intercepts, where the function touches or crosses the x-axis, the number of turning points, and determine the end behavior of the function. Sketch the function. hx ( ) = xx ( + )( x+ 4) Section 4.1

43 Chapter 4 00 Intercepts: x: x=0, x=-, x=-4 y: y=0 Crosses at all x intercepts due to odd multiplicity Number of Turning Points: For x>>0, f(x) goes to infinity, for x<<0, f(x) goes to negative infinity

44 CHAPTER Find the domain and any horizontal, vertical, and oblique asymptotes Gx ( ) 3 x 1 = x x Section 4.

45 Chapter Gx ( ) 1 ( 1)( + 1) ( 1)( + 1) ( + 1) = = = = 3 x x x x x x x x x x x x(1 x) xx ( 1) x Domain: All reals except x=0,x=1, hole at x=1 VA: x=0 HA: none since (degree numerator)>(degree denominator) OA: y=-x-1 after long division

46 CHAPTER Go through the seven step process to obtain the graph of the function: Rx ( ) = x 7x 15 x 5x Section 4.3

47 Chapter 4 600

48 CHAPTER Go through the seven step process to obtain the graph of the function: Rx ( ) = x 3 x 4 Section 4.3

49 Chapter 4 800

50 CHAPTER Solve & Graph the solution set. ( x )( x 1) x 3 0 Section 4.4

51 Chapter ( x )( x 1) x 3 Critical pts: 3,, 1 Intervals: 0 (,1) 0 0 (1, ) (,3).5 0 (3, ) 4 0 (1, ) (3, )

52 CHAPTER 5 00 Find f gx ( ) and g f( x) x f( x) = ; gx ( ) = x+ 3 x Section 5.1

53 Chapter 5 00 x f( x) = ; gx ( ) = x+ 3 x f gx ( ) = x = = + 3x x x x x ( x + 3) 6 g f( x) = = = + x x x x + 3

54 CHAPTER Find the inverse of the function. g x ( ) = 3x 4 x Section 5.

55 Chapter x 4 g( x) = y = x 3y 4 x = y xy x = 3y 4 xy + 3y = x 4 yx ( + 3) = x y g x = ( ) = x 4 x + 3

56 CHAPTER Solve the equation. Express any irrational solutions in exact form. 4 9 x x + 5= 0 Sections 5.3 & 5.6

57 Chapter x x = = 0 x x let y = 7 x y + 11y + 5 = 0 ( y+ 1)( y+ 5) = 0 x x ( 7 + 1)(7 + 5) = 0 x x = 0 or = 0 x 1 x 7 = or 7 = 5 1 xln 7 = ln or xln 7 = ln 5 1 ln ln ( 5) x= or x= ln 7 ln 7 no real solution

58 CHAPTER Write the expression as a single logarithm x + log x 3 x + log 7 x+ 6 x 4 x+ Section 5.5

59 Chapter x + x 3 x + 7x + 6 log log x 4 x+ ( x )( x 1) ( x+ 6)( x+ 1) = log log ( x )( x+ ) x+ ( x 1) ( x+ ) x 1 = log = log ( x + ) ( x + 6) x + 6

60 CHAPTER What will a $90,000 house cost 5 years from now if the price appreciation for homes over that period averages 3% compounded annually? Section 5.7

61 Chapter P = 90, 000 t = 5 r = 0.03 n = 1 r A= P 1+ n A = nt 90, 000(1.03) 5 A 104, Approximately 104, dollars