This paper circulates around the core theme of a) Can the de nition of f(x) when x 6= 1 be simpli ed? If yes, what is the simpler expression? together with its essential aspects. It has been reviewed and purchased by the majority of students thus, this paper is rated 4.8 out of 5 points by the students. In addition to this, the price of this paper commences from £ 99. To get this paper written from the scratch, order this assignment now. 100% confidential, 100% plagiarism-free.
Question 1. 3+5=8 marks
b) The equation x2 6x + y2 + 8y = 24 describes a circle.
i `Complete the square` to write the equation in form (x a)2 + (y b)2 = r2
ii Write down the coordinates of the centre of the circle and its radius.
iii What are the coordinates of the uppermost point of the circle?
Question 2. 3+2+4+4=13 marks
Consider the function with piecewise de nition
a) Can the de nition of f(x) when x 6= 1 be simpli ed? If yes, what is the simpler expression?
b) Sketch the graph of f(x) carefully for x between -5 and 3.
c) What is the domain of this function? What is its range? Justify your answers.
d) Is f(x) continuous? Assess this property formally.
Question 9. 4+5+2=11 marks
A particle moves along a number line so that its position at time t is given by
s(t) = t3 10t2 + 12t (t 0)
where s is in centimetres and t in seconds.
a) When does the particle change direction ? (i.e. when does its velocity change from nega-
tive to positive or vice versa?)
b) When is the particle moving to the right?
c) What is the furthest left the particle attains?
total 90 marks
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