Test 1
2004, Fall

Version A

Elementary functions. 30 points.

Sketch the graph and give the domain of the following functions!

2x-1, 	(((x-1))^2)+2, 	(1/(x+2)), 	(Sqrt[x]), 	(x^(1/3)), 	cos2x, 	tanx, 	(Subscript[log, 2])x, 	(2^x), 	(3^(-x)).

Algebraic rules. 20 points.

Find the following values!

((sinπ)/2), 	((cosπ)/4), 	((tan2π)/3), 	((tanπ)/4), 	(81^(1/4)),	 
(Subscript[log, (1/2)])16, 	lg0.01,	 	(Subscript[log, 3]) (1/9), 	(10^lg3), 	(Subscript[log, 5])25.

Equations. 20 points.

Find x that satisfies the following equation!

a) (Subscript[log, 2])x =3

b) (x^3)= -8

c) (3^x) = (1/9)

d) sinx = (1/2)

e) (Sqrt[x])= 3

Transformations. 15 points.

Which transformation steps on the graph of the function (2^x) are required to get the graph of f(x) = 1 - (2^(-x))? Make a sketch of the steps!

Inverse function. 15 points.

Find the inverse function of f(x) = (((x - 2))^3) -1! Plot the graph of f(x) and (f^(-1))(x)!