Q1.)

Given the functionf(x) =3x1/x+2determine any vertical or horizontal asymptotes.

Hint: Consider the value off(x) asxgoes to2and2+, and asxgoes toand +. [4 marks]

Q2.)

The Taupo triathlon consists of 3 phases, a 3.8km swim, 180km bike ride, and a 42.2km run. A competitor swims at a steady speed of 4.47km/h, cycles at a steady speed of 36km/h, and

runs the final leg at a average steady speed of 11.25km/h.

(a)Assuming no time is lost in any of the transitions, develop a piecewise function that will give you the athlete's distance coveredD(t) in kilometres in terms oft, theelapsed timein hours from the beginning of the race. [3 marks]

(b)8.5 hours after beginning the race, what phase of the triathlon was the athlete in, and how far had they gone in this phase? [2 marks]

Q3.)

a.)Determine whether each of the following is a function. If it is a function, give the range of the function. If it is not a function, explain why not.

(i)f:RR, f(x)=|x+1|

(ii)g:[0,)R,g(x)=x1

b.)

Consider the two functions f(x)=1/x+3 and g(x)=2/x-1. Find the domain and composite function

(fg)(x).