Description

Problem 1
(1+1+1+1+3+3 points)
Draw the graphs of the following equations in two variables x and y.
a) −3x + 2y = 2
b) x = 1
c) (x + 2)2 = 2(2y + 1)
d) (x + 2)2 + (y− 3)2 = 6
e) For each of the examples above, determine whether it is the graph of a function y = f(x). If so, find f(x), its domain, and its range.
f) For each of the examples above, determine whether it is the graph of a function x = g(y). If so, find g(y), its domain, and its range.
Problem 2
(10 points)
Let f(x) = 2x/2. Find the inverse function of f, denoted f−1, and state domain and range of f and f−1.
Note that f−1 is common symbolic notation for the inverse function. It does, however, not denote the function 1/f(x)!
Problem 3
(2+2+2+2+2 points)
Compute following limits
a) limx→1×2 + 2x− 2
b)
c)
d)
e)