MTH 111/URI

Spring 1998

University of Rhode Island

Exam #1

 

1.   Simplify (2 + 7i)/(4 - i)  and  i182

2.   Solve for x and write the solution set in the interval notation: |2x-1|>5.

3.   Find the domain and the range of f(x) = x2 + 4x - 5 .

4.   Find the standard equation of the circle which has the center at the midpoint between (2,3) and (-4,7) and radius r = 7.

5.   For the function f(x) = x2 + 2, find and simplify the difference quotient (f(x+h) - f(x))/h .

6.   Find the inverse of the function f(x) = (x + 2)/(2x - 5). What is domain of the inverse function?

7.   Find g(f(x)) and f(g(x)) if f(x) = 2x + 4 and g(x) = x2 - x.

8.   Find the equation of the line which goes through (2,1) and is perpendicular to the line  2y + 4x - 1 = 0. Sketch the graph of this line.

9.   Identify the vertex, axis of symmetry, x-intercept(s), y-intercept, and the range for f(x) = x2 + 7x + 6. Sketch the graph of this function.

10.  Write y = 2x2 - 4x - 6 in the form y = a(x - h)2 + k and use it to find the vertex and x-intercept(s) of this function.