Let f be a function defined on all of r that satisfies the
additive condition f(x+y)=f(x)+f(y) for all x, y∈r.
(a) show that f(0)=0 and that f(−x)=−f(x) for all x∈r .
(b) let k=f(1). show that f(n)=kn for all n∈n, and then prove that
f(z)=kz for all z∈z. now, prove that f(r)=kr for any rational
number r.
(c) show that if f is continuous at x=0, then f is continuous at every point
in r and conclude that f(x)=kx for all x∈r. thus, any additive
function that is continuous at x=0 must necessarily be a linear function
through the origin.

Finally, the arena decides to offer advertising space on the jerseys of the arena’s own amateur volley ball team. the arena wants the probability of being shortlisted to be 0.14. what is this as a percentage and a fraction? what is the probability of not being shortlisted? give your answer as a decimal. those shortlisted are entered into a final game of chance. there are six balls in a bag (2 blue balls, 2 green balls and 2 golden balls). to win, a company needs to take out two golden balls. the first ball is not replaced. what is the probability of any company winning advertising space on their volley ball team jerseys?

Question 3 (essay worth 10 points) (03.06 mc) part a: max rented a motorbike at $465 for 5 days. if he rents the same motorbike for a week, he has to pay a total rent of $625. write an equation in the standard form to represent the total rent (y) that max has to pay for renting the motorbike for x days. (4 points) part b: write the equation obtained in part a using function notation. (2 points) part c: describe the steps to graph the equation obtained above on the coordinate axes. mention the labels on the axes and the intervals. (4 points)

For problems 29 - 31 the graph of a quadratic function y=ax^2 + bx + c is shown. tell whether the discriminant of ax^2 + bx + c = 0 is positive, negative, or zero.