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Name:_________________________Date:__________________________ Trigonometry Chapter 1 Review Sheet (1.1-1.4&1.6) Put the following into interval notation. Then describe it as bounded or unbounded. Interval notation Bounded or unbounded? x<3 unbounded (-, 3) [-2,9] bounded x -22 [-22,) unbounded -12 < x < -2 (-12, -2) bounded 0 < x 15 (0, 15] bounded -2 4 9 What makes an interval bounded? If the interval has an endpoint on each end, it is bounded. What makes an interval unbounded? If the interval continues without end it is unbounded. In other words, the interval contains an symbol. Describe when you use ( ) or [ ] in interval notation. You use parentheses for < and >. You use brackets for and . Define the following: Rational number – Any number that can be expressed as a fraction. Integer – Any number that can be expressed as a fraction with a denominator of 1. Whole number – Positive integers and zero. Example: 0, 1, 2, 3, … Natural number- Counting numbers. Example: 1, 2, 3, 4, 5,… (Whole numbers except for zero.) Trigonometry Chapter 1 Review Sheet 1.1-1.4 & 1.6 Page 1 of 8 Categorize the following numbers as rational, irrational, integer, whole numbers, counting numbers. Remember, some numbers may fall in more than one category. 13, -2.45, -e, 121/4, -8, 2, 16, 0, 5.111, -4.353353335..., 14, 3 2, Rational Numbers: Irrational Numbers: Integers: 13, 16, 0, /3, 6 13, -8, 16, 0, 6 13, -2.45, 121/4, -8, -e, 2, 16, 0, 5.111, 12/3, -4.353353335..., 6 14, 3 2 Whole Numbers: 12 12 /3, Counting Numbers: 12 /3, 6 13, 16, 12 / 3, 6 What are four possible methods of solving quadratic equations? Quadratic Formula, Completing the Square, Extracting Roots, Factoring/Zero Product Property What is the difference between an identity and a conditional equation? An identity has infinitely many solutions (any real number you can think of is a solution). A conditional equation has a limited number of solutions. When solving what kind of equations must you check your answers for extraneous solutions? Rational Equations, Absolute Value equations and Radical Equations Solve the following equations. Be sure to check for extraneous solutions. There may be problems that are identities and there may be problems with no solution. If that is the case, write IDENTITY or NO SOLUTION. 3(x + 3) = 5(1 – x) – 1 (x+2)2 + 4 = (x + 3)2 x = -5/8 x2 + 2(3x – 2) = x2 + 6x – 4 x = -1/2 100 – 4x = 5x + 6 + 6 3 4 x = all real numbers (Identity) x = 10 Trigonometry Chapter 1 Review Sheet 1.1-1.4 & 1.6 Page 2 of 8 10x + 3 = 1 5x + 6 2 6 - 2 = 3(x + 5) x x+3 x2 + 3x x=0 x = -3 x2 – 2x – 8 = 0 (x + 3)2 = 81 x = 4 or x = -2 x = 6 or x = -12 x + 2 = x (x – 2)2= x2 – 4 x=2 x = 2 , x = -1 4x4 – 18x2 = 0 | x + 1 | = x2 + x x=1 x = 0, x = 32/2 Write out the following formulas: Distance formula: Midpoint formula: x 1 + x 2 , y1 + y 2 d = (x2 – x1) 2 + (y2 – y1)2 2 Slope formula: m= y2 – y 1 x2 - x 1 Trigonometry Chapter 1 Review Sheet 1.1-1.4 & 1.6 Page 3 of 8 2 Determine the distance, midpoint and slope of the line segment that connects the following two points. Be sure to simplify all fractions and all radicals. Distance: Midpoint: Slope: (6,5) & (-8,3) 102 (-1,4) 82 (1.9, 1.4) 1 /7 (-2.1, 5.4) & (5.9, -2.6) -1 Fill in the missing sections of the chart below regarding circles: Center Radius Standard Form: General Form: 2 2 2 2 (x – h) + (y – k) = r Ax +By2+Cx+Dy+E = 0 (2,3) 1 (x – 2)2 + (y – 3)2 = 1 x2 + y2 - 4x - 6y + 12 = 0 (-2,0) 5 (x + 2)2 + (y – 0)2 = 25 x2 + y2 + 4x - 21 = 0 (x – 2)2 + (y + 3)2 = 8 x2 + y2 - 4x + 6y + 5 = 0 /3 (x -1/2)2 + (y + 3/8)2 = 1/9 576x2 +576 y2 - 576x + 432y - 79 = 0 (3, -6) 311 (x – 3)2 + (y + 6)2 = 99 x2+y2-6x+12y-54 = 0 (0,5) 41 x2 + (y - 5)2 = 41 2x2+2y2-20y-32=0 (2, -3) (1/2, -3/8) 22 1 Fill in all information below for the circle whose diameter is the line segment between (-2,2) and (4,-10) (1,-4) 35 2 2 (x – 1) + (y + 4) = 45 Trigonometry Chapter 1 Review Sheet 1.1-1.4 & 1.6 Page 4 of 8 x2 + y2 - 2x + 8y - 28 = 0 Complete the following charts with the appropriate procedures on determining symmetry: To determine To determine To determine x-axis symmetry y-axis symmetry origin symmetry Replace y with (-y) Clean up Check to see if new = old Replace x with (-x) Clean up Check to see if new = old Replace x with (-x) Replace y with (-y) Clean up Check to see if new = old Determine what type of symmetry the following graphs will have (if any). 3x + 2y = 12 x-axis: y-axis: Origin: 3x + 2(-y) = 12 3(-x) + 2y = 12 3(-x) + 2(-y) = 12 No No No y + 2x2 = 0 x-axis: y-axis: 2 Origin: 2 (-y) + 2x = 0 y + 2(-x) = 0 (-y) + 2(-x)2 = 0 No Yes No y= x-axis: 2x x2 – 4x y-axis: 2x (-y) = 2 x – 4x Origin: 2(-x) y= 2 (-x) – 4(-x) 2(-x) (-y) = 2 (-x) – 4(-x) No No No y = x3 x-axis: y-axis: (-y) = x 3 Origin: 3 y = (-x) (-y) = (-x)3 No Yes No 2y2 = x3 x-axis: y-axis: 2 2(-y) = x Yes 3 Origin: 2 3 2y = (-x) 2(-y)2 = (-x)3 No No Trigonometry Chapter 1 Review Sheet 1.1-1.4 & 1.6 Page 5 of 8 Complete the following charts with the appropriate procedures on determining x and yintercepts: To determine To determine x-intercept y-intercept Replace y with zero. Replace x with zero. Determine the x and y-intercepts of the following graphs. Be sure to write your answer as an ordered pair (#,0) and (0,#).: y = 25 – x2 y-intercepts: x-intercepts: (0) = 25 – x2 y = 25 – (0)2 (5,0) & (-5,0) (0,5) x2 + y2 – 12x + 20 = 0 y-intercepts: x-intercepts: x2 + (0)2 – 12x + 20 = 0 (0)2 + y2 – 12(0) + 20 = 0 (2,0) & (10,0) none xy = 7 y-intercepts: x-intercepts: x(0) = 7 (0)y = 7 none none Write equations of the various forms of linear equations: Slope-intercept form: Point-Slope form: y = mx + b Standard Form: (y – y1) = m(x – x1) General Form: Ax + By = C Ax + By + C = 0 Trigonometry Chapter 1 Review Sheet 1.1-1.4 & 1.6 Page 6 of 8 What must you remember about the coefficients of the Standard Form and the General Form? They must be integers. They cannot be fractions. What does a vertical line’s equation look like? x What is the slope of a vertical line? There =# is no slope. What does a horizontal line’s equation look like? y What is the slope of a horizontal line? Slope =# = 0. Fill in the various forms of the linear equations provided the given information: The line that has a slope of 5 and passes through (0,9) Slope-intercept form: Point-Slope Form: Standard Form: General Form: y = 5x + 9 y – 9 = 5(x – 0) The line that passes through (2,1) and (14,6) Slope-intercept form: Point-intercept form: y = 5/12x + 1/6 y – 1 = 5/12(x – 2) or 5 y – 6 = /12 (x – 14) 5x – y = -9 Standard form: 5x -12y = -2 5x – y + 9 = 0 General form: 5x -12y + 2 = 0 The line that perpendicular to y = 2/3x – 6 and passing through the point (1,-5) Slope-intercept form: Point-Slope Form: Standard Form: General Form: y = -3/2x + 13/2 y + 5 = -3/2(x – 1) 3x + 2y = 13 The vertical line passing through the point (-5,2) Slope-intercept form: Point-Slope Form: Standard Form: None None (because there (because there is no slope) is no slope) x = -5 Trigonometry Chapter 1 Review Sheet 1.1-1.4 & 1.6 Page 7 of 8 3x + 2y – 13 = 0 General Form: x+5=0 Graph the following. Use intercepts and symmetry as an aid in graphing. Then determine the range and domain. y = x2 – 2x y = x3 + 3 y=x–3 D: [-1,) R: (-, ) D: [3,) R: (0, ) D: (-,) R: (-, ) y = –| x – 6| y = –2x – 3 x=5 D: (-, ) R: (-, 0] D: (-,) R: (-, ) D: x = 5 R: (-, ) x2 + y2 = 9 y = x – 5 y = -(x - 3)2 + 1 D: [-3,3] R: [-3,3] D: [0,) R: [-5, ) D: (-, ) R: (-, 1] Trigonometry Chapter 1 Review Sheet 1.1-1.4 & 1.6 Page 8 of 8