1. [7 marks] Consider the function, f[x) = 2/ x2. (a) Graph the function f[x) (b) Hence, using translations, reections etc., graph 2 (x- 3? Make sure that you show and label the intermediate graphs. g(x) 23+ 2. [6 marks] For each of the following functions, give the domain and range using interval notation, showing your reasoning. (lNhen the domain is not specified, we adopt the convention that the domain consists of all numbers for which the function is defined.) (a) f(x} = 3" :3 (b) f(x}= x/x25x+6 3. [6 marks] Find the following limits, if they exist, showing all the working. ( ) 1, x2 + x 2 a x39: 3(x + 2) . x + 2 (b) :51}. 3x2 + 1 4. [8 marks] Consider the function defined by 2/3:2 if x 4 Graph the function. Find all values of x where the function is discontinuous. Justify your answer by addressing all the conditions for continuity. 5. [12 marks] Find the derivatives of the following functions, simplifying your answers. (a) f(x} = 252/3 + m2 5 21 (b)g(rJ=3+1 (c) hm = [(ch2 +1)(x 3) 4/3 6. [6 marks] Find {and simplify) the equation of the tangent line to the graph of _ x+2 x4 atx=2. y 7. [5 marks] 10% of the marks for this assignment are reserved for presentation. Note: There are penalties for late assignments. You must contact your tutor before the due date if you have difficulties making the deadline