Please help me. i need help on these questions

1. A transformed cosine function, given by, () = [2 + 60] +

has a maximum value of 9 and a minimum value of 5. There is no reflection about the x-axis, so that a > 0.

a ) [2 marks] Determine the value of c.

(a) b) [2 marks] Determine the value of a.

b) c) [2 marks] List the transformation that was applied to the present function () = () ()

d) [4 marks] Sketch the graph of () (). { | 180 180} in pencil and paper.

2 ) Given the following different presentations of a relation, explain how to tell if the underlying relation is a function in each case. Give an example of each.

a) [5 marks] Graphs:

b) [5 marks] Tables of values:

3) A petri dish contains an initial sample of twenty bacteria. After 1 day, the number of bacteria has tripled. (a) [1 mark] Determine the population after each day for 1 week.

(b) [1 mark] Write an equation to model this growth.

(c) [2 marks] Graph the relation using pencil and paper. Is it a function? Explain why or why not.

(d) [2 marks] Assume this this trend continues, predict the population after 3 weeks.

4) [4 marks] Prove the identity () (1/() + 1/()) = () + ()