Directions: Please help with the following visual questions.
For the multiple choice ones you can simply show the answer to save time however please provide WORK for my understanding for the non-multiple choice questions!
Note: THIS ISNT FOR AN ASSIGNMENT BUT MERELY FOR MY OWN UNDERSTANDING AND COMPREHENSION! PLEASE BE ORGINAL! THIS IS FOR PRACTICE.
\fEquation of a line Slope intercept form: y = mx +b Vertical line: x = c (slope is undefined) Point-slope form: y-y, = m(x-x,) Horizontal line: y = c (slope is 0) 38. Use slope-intercept form to find the equation of the line having a slope of 3 and a y-intercept of 5. 39. Determine the equation of a line passing through the point (5, -3) with an undefined slope. 40. Determine the equation of a line passing through the point (-4, 2) with a slope of 0. 41. Use point-slope form to find the equation of the line passing through the point (0, 5) with a slope of 2/3. 42. Find the equation of a line passing through the point (2, 8) and parallel to the line y = =x -1. 43. Find the equation of a line perpendicular to the y- axis passing through the point (4, 7). 44. Find the equation of a line passing through the points (-3, 6) and (1, 2). 45. Find the equation of a line with an x-intercept (2, 0) and a y-intercept (0, 3).For each of the following, express the value for "y" in radians. 76. y = arcsin- V3 2 77. y = arccos(-1) 78. y = arctan(-1) 13 Example: Find the value without a calculator. cos arctan V61 Draw the reference triangle in the correct quadrant first. 5 Find the missing side using Pythagorean Thm. 6 Find the ratio of the cosine of the reference triangle. cos 0 = - 6 61 For each of the following give the value without a calculator. 63. tan arccos WIN 64. sec sin - 12 13 65. sin arctan 12 66. sin sin-Angles in Standard Position 48. Sketch the angle in standard position. a. b. 230 C. d. 1.8 radians 6 9 Reference Triangles 49. Sketch the angle in standard position. Draw the reference triangle and label the sides, if possible. a. b. 225* C. d. 30Limits to Infinity A rational function does not have a limit if it goes to + co, however, you can state the direction the limit is headed if both the left and right hand side go in the same direction. Determine each limit if it exists. If the limit approaches co or -co, please state which one the limit approaches. 2+ x 2 98. lim 99. lim = 100. lim x+l 1-x sin xTrigonometric Equations: Solve each of the equations for 0 S x 5 2 3 Domain and Range Find the domain and range of each function. Write your answer in INTERVAL notation. 30. f(x) = x -5 31. f(x) =-Vx+3 32. f(x) = 3sin.x 33. f(x) = 2 x - 1 Inverses To find the inverse of a function, simply switch the x and the y and solve for the new "y" value. Example: f(x) = Vx+1 Rewrite f(x) as y y = Vx+1 Switch x and y x = Vy+1 Solve for your new y (x)' = (Vy+1) Cube both sides x =y+1 Simplify y=x'-1 Solve for y f'(x)= x' -1 Rewrite in inverse notation Find the inverse for each function. 34. f(x) = 2x+1 35. f(x) = w / 4\f78. lim vx' + 4 79. lim cos.x 16 x+x-6 80. lim HINT: Factor and simplify. 81. lim - x+3 /x+1-1 82. lim HINT: Rationalize the numerator. I-+0 X 83. lim- 3-x 84. lim 2(x+ h) - 2x 1+3x- -9 h One-Sided Limits Find the limit if it exists. First, try to solve for the overall limit. If an overall limit exists, then the one-sided limit will be the same as the overall limit. If not, use the graph and/or a table of values to evaluate one-sided limits. 85. lim x-5 86. lim 1-+5* x- - 25 14-3 1 x 2 - 9 x - 10 3 87. lim 88. lim 1 10* x -10 x+5Vertical Asymptotes Determine the vertical asymptotes for the function. Set the denominator equal to zero to find the x-value for which the function is undefined. That will be the vertical asymptote. 89. f (x) = - 90. f (x) = = 2+x 72 -4 91. f(x) = - x' (1- x) Horizontal Asymptotes Determine the horizontal asymptotes using the three cases below. Case I. Degree of the numerator is less than the degree of the denominator. The asymptote is y = 0. Case II. Degree of the numerator is the same as the degree of the denominator. The asymptote is the ratio of the lead coefficients. Case III. Degree of the numerator is greater than the degree of the denominator. There is no horizontal asymptote. The function increases without bound. (If the degree of the numerator is exactly 1 more than the degree of the denominator, then there exists a slant asymptote, which is determined by long division.) Determine all Horizontal Asymptotes. 92. f(x) = * - 2x+ 1 x +x-7 93. f (x) = 5x - 2x2 + 8 4x - 3x' +5 94. f(x) =- x3 - 7 Determine each limit as x goes to infinity. RECALL: This is the same process you used to find Horizontal Asymptotes for a rational function. ** In a nutshell 1. Find the highest power of x. 2. How many of that type of x do you have in the numerator? 3. How many of that type of x do you have in the denominator? 4. That ratio is your limit! 2x -5+4x2 2.x - 5 7x+6-2x' lim lim lim 95 3-5x+ x 96. 3-5x+ 3x2 97. 3+14x+.x
