Unit Test 2.pdf

Unit Test 2.pdf - Unit Test 2 Course Advanced Functions 12...

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Unformatted text preview: Unit Test 2 Course: Advanced Functions 12, MHF4U Date: ………….……….. Time: …… hours + Name: _____________________________________ Examination Marks Breakdown Knowledge: 12 Application: 16 Communication: 10 Inquiry/Thinking: 5 Total Marks: / 43 Short Answers:[ / , Long Answers:[ 1. 2. 3. 4. 5. / , Total:[ / Give EXACT answers for all questions unless otherwise indicated. Neat, complete solutions are required. Read all questions carefully. For full marks, correct mathematical form is necessary. You are NOT allowed any books, or electronic devices in the exam (No textbooks, dictionaries, cell phones, ipods, mp3 players) 6. You are allowed to bring a calculator, ruler, high-lighters, white-out and pens. 7. Write your exam in pen. 8. You have 2 hours to complete the exam. Please sign here prior to the start: Short Answers: Answer each question in their designated area: Show your work for every question: 1) Express that if the following statement is true or false. Write the complete right answer for each question: (4 Marks, K:2, A:2) The function has only one vertical asymptote at x = –5 . 2 + 9 + 20 = 0, ( + 5)( + 4) = 0, 2. What is true about the function C:1) ℎ = −5 = −4 . Explain the end behaviour ? (3 Marks, T:2, 3 + 1 = −(0+ ) + 1 = 0− + 1 = +1− →+∞ ∞−3 3 → −∞, ℎ lim () = − + 1 = −(0− ) + 1 = 0+ + 1 = +1+ →−∞ −∞ − 3 → +∞, ℎ lim () = − 3. Which of the following is true? (2 Mark, K:1, T:1) . 4. The horizontal asymptote of the function is : (1 Mark, K:1) . ℎ ℎ ℎ . , 12 =4 3 (2 Mark, K:1, T:1) 1 − = 0, ℎ(0) = 2 4 4 1 . (0) = − =− = (0)2 − 7(0) − 8 −8 2 6. Based on the form of the rational function, how can you identify the vertical, horizontal or oblique asymptotes, or no asymptotes? (4 Mark, T:1, C:3) + = 0, + ≠ 0, ℎ () = ±∞ ℎ . =− → ±∞ () = , ℎ ℎ ℎ . () = ℎ ℎ: ℎ ℎ 1 ℎ ℎ ℎ . ℎ ℎ + + ℎ ℎ: ℎ ℎ ℎ 1 ℎ ℎ ℎ Long Answers: Answer each question in their designated area: 1) Solve, 0 , algebraically and show your work. (6 Mark, K:2, A:4) +3 ≥0 +1 + 1 = 0, ℎ = −1, () = ( ) + 3 = 0, ℎ = −3, () = 0 () + ℎ ≥ 0, : (−∞, −3] ∪ (−1, +∞) −3 0 − −1 + 2)Draw a labeled sketch for a rational function with the following conditions. (6 Marks, K:2, C:2, A:2) ● is a reciprocal of a linear function ● horizontal asymptote is y = 0 ● vertical asymptote is x = 1 ● y-intercept is -1/2 ● only has intervals of decrease = 1, ℎ ℎ ( − 1) = 0, ℎ lim () = 0 →∞ 1 1 − − , ℎ(0) = − 2 2 1 () = 2( − 1) 3) for the function find the following: (6 Marks, K:2, A:4) a) Domain and Range Domain: 1 1 2 2 2 − 1 = 0, ℎ = , + 1 = 0, ℎ = −1, : − {−1, } Range: : (−∞, − 16 ∪ (0, +∞) 9 b) X, and y intercept (0) = 2 = 2 = −2, − (0, −2) (−1)(1) (2(0) − 1)((0) + 1) 2 () = 0, = 0, , − (2 − 1)( + 1) c) Vertical and horizontal asymptote : lim () = 0+ , lim () = 0+ , →+∞ →−∞ : lim + () = +∞, lim − () = −∞, →+ 1 2 lim () = −∞, →−1+ d) Graph the function 1 →+ 2 lim () = +∞, →−1− 4) Explain what rational functions are. How many types of rational functions have we learnt in chapter 3. Bring 3 examples for every case and show them by writing the formula and graph them. (5 Marks, K:1, C:4) Any function that is defined by rational fraction is rational function. (−3)(+4) 5) Solve (−1) = (+3)(2+6) (4 Marks, A:4) (+5) ( − 3)( + 4) ( + 3)(2)( + 3) = ( − 1) ( + 5) ( − 3)( + 4) (2)( + 3)2 = ( − 1) ( + 5) ( 2 + − 12)( + 5) = (2)( 2 + 6 + 9)( − 1) ( 3 + 6 2 − 7 − 60) = (2 3 + 10 2 + 6 − 18) ( 3 + 4 2 + 13 + 42) = 0 ≈ −3.6166 Communication Rubric: Achieveme Level 0 nt 0-49% Category Level 1 50-59% Level 2 60-69% Level 3 70-79% Level 4 80-100% Knowledge No / evidence Understan ding Shows a limited understandin g of the concepts Shows some understandin g of the concepts Shows an understandin g of the concepts Shows a high degree of understanding of the concepts Applicatio n No evidence Shows a limited connection between trigonometry and profession. Shows some understandin g of the scenario and answers few questions Shows a clear understandin g the scenario and calculating the problems Shows a good understanding of the problem and solved the questions Communic ation No evidence Report & presentation shows limited clarity Report & presentation shows some clarity Report & presentation shows clarity Report & presentation shows a high degree of clarity ...
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  • Fall '19
  • lim, Rational function

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