MATHS1001 - Modelling and Change Assignment - Federation University

Assignment Task

Questions

1. a. The function f f is defined as follows:

f f (0) = 2, f f(1) = 4, f f (2) = 6, f f(3) = 4, f f(4) = 8 f f(5) = 8,f f(6) = 4, f f(7) = 6, f f(8) = 6,f f(9) = 8

1. What are the domain and range of f?

2. Evaluate f f 1 2 f f (kk) and call the answer c. [Remember that the value of k that you need to use is the last digit of your student number]. Now define a function gg on (- ∞ ∞) by gg (xx) = xxkk + xxcc.

3. Show whether gg is odd, even, or neither.

1. b. Write the equation of the line that passes through the points (5, 11) and (c, -7). [Remember that the value of c was obtained above].

2. Determine any intercepts of the axes. Draw a graph of the line found above labelling where it crosses any axis.

3. Explain whether the line is decreasing, increasing or neither.

2. a. In the picture below you can see two methods a wind direction is measured. The first method (method A) designates the direction of a wind by specifying the angle at which it blows measured anticlockwise from the East. In contrast, the second method (method B) indicates the angle from which the wind is blowing, measured clockwise from the North. Both methods utilize values within the range of 0° to 360°.

i) Derive a piecewise formula expressing Θθ AA in terms of ΘθBB.

ii) Draw a graph depicting the angle Θθ AA as a function of the angle ΘθBB.

b. Use a function grapher to graph a function h (xx) = xx3 − 3xx2. With the aid of this graph, write a formula for the graphs of the two functions pp(xx) and ww(xx)) shown below. Justify your response.

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