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 x
2 + 2 x − 2
b) lims→0
s
3
s
c) limt→4
t
2−16
t−4
d) limv→2
2 − v
1
2 −
1
v
e) limy→0
√
2−y−
√
2+y
−4y