Test 1
2001, Fall

Version A

Definitions. 10 points.

Give the definition of a function, the domain and range.

Algebraic rules. 5+5 points.

Compute and simplify the following expressions so that only positive exponents remain!

(((x^2) y+x (y^2))/xy), 	((1-(x/(x-y)))/(1-((y-x)/(x+y)))).

Evaluation. 3+2+2+2+2+4 points.

Evaluate the following expressions!

(((5^3) (3^4))/((Sqrt[81]) 25)), 	((1/64)^(1/3)), 	(Subscript[log, 4]) 2, 		(10^(lg 4)), 		((sin π)/6),	 	(((Subscript[log, (1/3)]) 2)/((Subscript[log, 3]) 8)).

Functions. 5+5+5+5+5+5+5 points.

Plot the graph of the following functions!

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

Transformations. 5+5 points.

Use elementary transformations to plot the following functions!

cos3x, 		1-(2^x).

Equations. 5 points.

Solve the following system of equation!

y+2x = -1, 	4x-3y = 2.

Parabola. 10 points.

Determine the peak point and zero points and draw the graph of the parabola: y = (x^2)-3x-4!

Inverse function. 5 points.

Find the inverse function of f(x) = (((x-1))^5)+2!