Problem 1

Draw the graphs of the following equations in two variables x and y.

1. −3x + 2y = 2
2. x = 1
3. (x + 2)² = 2(2y + 1)
4. (x + 2)² + (y− 3)² = 6
5. 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.
6. 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

Let f(x) = 2^x/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

Compute following limits

1. a) lim_x→1x² + 2x− 2

b)

c)

d)

e)