# MTH 111/URI

### Spring 1998

#### University of Rhode Island

## Exam #1

**1. **Simplify (2 + 7i)/(4 - i) and i^{182}

**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) = x^{2} + 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)
= x^{2} + 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) = x^{2} - 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) = x^{2} + 7x + 6. Sketch the graph of this function.

**10. **Write y = 2x^{2} - 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.