(d) Find the domain and the range of f (x) = x2 16 5 . [9]
2. Consider the quadratic function f (x) = 3 + 2x x2 . (a) Express f (x) in standard form. (b) Find the coordinates of the vertex and indicate whether it corresponds to the maximum or the minimum of f . (c) Find the x and y intercepts. (d) Sketch the graph of f (x) using the information above. [9]
3. (a) Let f (x) = 53x 4 2. Find the inverse function f 1 (x). (b) Let f (x) = ex+1 and g (x) = ln(x 1). Find g f and determine its domain. [12] 4. Find the solutions of the following equations: (a) 22x 2x+3 20 = 0 (b) log3 x + log3 (x + 2) 2 = 0 MATH 201 [12] 5. Final Examination December 2012 Page 2 of 2 Find the solutions of the following equations: (a) 2 2x 8x = 0 (b) log5 (x + 1) log5 (x 1) = 2 [9] 6. (a) Find the radius of the circle if its sector with a central angle 1 = radian has an area A = 9 m2 . 2 (b) A car s wheels are 70 cm in diameter. What is the speed of the car in km/hour if the wheels rotate at 180 revolutions per minute ? [12] 7. Solve the triangle ABC (i.e. nd the missing sides and angles) (a) A = 30 B = 70 b = 30 cm (b) A = 53 b = 15 cm c = 20 cm [9]
8. 1 (a) Find the amplitude period and phase shift of y = 3 sin[ (x 3 )]
(b) A ladder leans against a vertical wall of a building so that the angle between the ground and the ladder is 72 and its bottom on the ground is at 3 m from the wall. How long is the ladder? How high does it reach? [6]
9. Verify the identities sin x 1 cos x =0 sin x 1 + cos x cot x (b) csc x sin x = sec x (a) [10] 10. Solve the following trigonometric equations in [0 2 ] (a) (b) [5] 11. sin2 x + sin x = cos2 x sin 2x cos x + cos 2x sin x = 1 Bonus Question If a function f (x) is dened for all real x and has an inverse f 1 (x) does it necessarily follow that also g (x) = [f (x)]2 has an inverse g 1 (x) ? Explain why it does or give an example when it does not.
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BENCHMARK – EFFECTS OF CHILDHOOD TRAUMA WORKSHEET
Academic Level University Subject Healthcare Type of Paper Other (Not listed) Paper Format APA Assessment Traits Benchmark Requires Lopeswrite Assessment Description Complete the “Effects of Childhood Trauma Worksheet” document attached. While APA format is not Read more…