Project #55047 - Functions, vectors (2 questions)

Q1:

(a) This part of the question concerns the function f(x) = |x + 1| − 3.

(i) Explain how the graph of f can be obtained from the graph of y = |x| by appropriate translations. (You are not asked to sketch any graphs at this stage, although you may find it helpful to do so.) [2]

(ii) Write down the image set of the function f, in interval notation. [2]

(b) This part of the question concerns the function g(x) = |x + 1| − 3 (−1 ≤ x ≤ 4). The function g has the same rule as the function f in part (a) , but a smaller domain.

(i) Sketch the graph of g, using equal scales on the axes. Mark the coordinates of the endpoints of the graph. What is the image set of g? [3]

(ii) Find the inverse function g −1 , specifying its rule, domain and image set. [6]

(iii) Add a sketch of y = g −1 (x) to the graph that you produced in part (b)(i)

 

Q2:

A boat has a speed of 4 m s −1 (relative to the surrounding water) and a heading of 170â—¦ . There is a current flowing from a bearing of 105â—¦ at a speed of 2.5 m s −1 . Take i to point east and j to point north.

(a) Express the velocity v of the boat relative to still water and the velocity w of the current in component form, giving numerical values in m s−1 to one decimal place. [7]

(b) Express the resultant velocity v of the boat in component form, giving numerical values correct to one decimal place. [3]

(c) Hence find the magnitude and direction of the velocity v of the boat, giving the magnitude to one decimal place in m s −1 and the direction as a bearing to the nearest degree. 

Subject Mathematics
Due By (Pacific Time) 01/28/2015 03:00 am
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