NIDES Pre Calculus 12 1. Approximately how many concepts did you study in this unit? 2. a) Which concept was the most challenging? b) Give an example to show your understanding of this concept. 3. Complete the chart below with 4 other concepts from this unit # Concept Show your understanding of the concept with an example. Remember that this is a grade 12 course so SW boy bia looking for higher level math work and example 1 Graphing a rational function that has a point of discontinuity. 2. When would you have a horizontal asymptote of: y=0 y = 1 3. What is any way of remembering the vertical OT asymptotes? 4. (5 marks) Unit 2 N2023 Calculus 12 Co rite the following graph in the form of: y = x-h +k Show your work! (2 marks) - 2 5. How are these two equations different when it comes to determining the horizontal asymptote? y = _ gtk vs y = _ gtk Choose integer values (other than zero and one) for a, h, and k. Graph your own rational function. (4 marks) ite your equation in the form of: y - x-h ax + k Equation: y = Asymptotes: Domain: Range:NIDES Precalculus 12 Idon - Soccer 7. Write the equation of a possible rational function given the following information: a) Vertical asymptotes at x = 14 and x-intercepts at 3 and -5. ent b) A vertical asymptote at x = -2, discontinuous point at (3, 2), and x-intercept at -7. c) A horizontal asymptote at y = =, a vertical asymptote at x=7, a discontinuous point that has an x value of 2, and x-intercept at -5. 8. Sketch the graphs of the following functions and show all asymptotes with a dotted line. Show your work as you should be able to graph WITHOUT a graphing calculator. State the x and y intercepts, asymptotes, point of discontinuity, domain and range. (5 marks) y = - x2+2x-15 x2-4x+3Precalculus 12 9. Solve algebraically for the exact values of x. Remember that exact value means leaving your hat are a answer in a form that the answer has not been rounded. Show your work. (2 marks each) x a) 4x 4x+21 b) 1= 2x+ 1 3x-1 10. A boat can travel at 28 km per hour in still water. The boat travels 24 km upstream against the current then turns around and travels the same distance back with the current. If the total trip took 2.5 hours, what is the speed of the current? Solve this question algebraically. Round answer to the nearest tenth. (3 marks)NIDES Precalculus 12 . Identify the transformations of the following from y = vx . show your work when isolating y. each lesson? Remember the concepts from unit 1 when doing this question! 2y - 6 = - V3x + 12 2 marks 12. Graph of the following function. Show clearly 3 coordinates. State the domain and range. (2 marks) y = 2Vx +5-4 13. Write the equation using information from the graph. Use the form y = avb(x-h) +k. Show your work as I should see substitution of the vertex and a point to determine the a or b value (not both). The vertex in this function is in QIll. (2 marks) work Equation: Unit 2s Precalculus 12 stions that are at the 14. Draw a linear function on the left graph. Please do not use an equation taught in the lessons. Write n? (5 marks ) the equation as y = mx + b. Both m and b must be integers other than 0, 1, and -1. Draw the function that would represent y = Jf(x) y = f(x) V= Vf(x ) y = List the domain and range of each graph. Domain f (x) : Domain f (x) : Range f (x) : Range f (x) : Determine the EXACT VALUES of any invariant points. Show your work in the space provided. Invariant Points: Unit 2NIDES Precalculus 12 15. Draw a quadratic function on the left graph. The vertex must be in Qlll or QIV with a positive "a" (5 marks) fraction between 1 and 2. ach lesson Write the equation as y = a(x - h)2 + k y = f(x) y = _ y = Vf(x) y = List the domain and range of each graph. Domain f (x) : Domain f (x) : Range f (x) : Range f (x) : Determine the EXACT VALUES of any invariant points. Show your work in the space provided. Invariant Points: Unit 2Sheldon Na's precalculus 12 of birth : And . 16. Solve each of the following algebraically for their exact values. (2 marks each) a) V8x +9 - 3 = 12 b) ;Vx- 7- 5=1 ease i c) V-7 - 5x - 3 = x 17. Write a possible equation for the following graph. Explain your reasoning. Unit 2