1. Suppose you are given a quadratic function:f(x) =ax2+bx+c.

(a)Supposea <0 andb <0. Prove that the function achieves a maxi-mum at a negative value ofx. What is the value ofxand the value off(x) at the maximum?

(b)Supposea >0 andb <0. Prove that the function achieves a mini-mum at a positive value ofx. What is the value ofxand the value off(x) at the minimum?

2) Find the domain and range off(x) =1/1+x and graph the function.

3) Find the domain and range of f(x) = 1/3+x + 3 and graph the function. Compare this to the graph in question 2 immediately above.

4) Suppose y=ax+b is a line with a > 0 and b > 0. Show that there is a line with slope1/athat intersects the original line at 90, i.e. the new

line is perpendicular to the original line.

Please provide explanation and steps as to how the answer came about. It'll be of great help. Thank you very much