**2. **Find the domain of

**3. **Find the standard equation of the circle which
center is at the point (1,1) and which
passes through the point (2,-1).

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

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

**6. **Identify the vertex, axis
of symmetry, x-intercept(s),
y-intercept,
and the range for y = 2x^{2} - 7x
- 4. Sketch the graph of this function.

**7. **Find x-
and y-intercepts
and all the asymptotes of the function f(x)
= (x^{2} - 4)/(3x^{2} + 11x - 4). Sketch
the graph of

this function.

**8. **Find the inverse function of the
function f(x) = 2^{x-1} - 4.
Sketch the graphs of f
and f ^{-1} on
the same coordinate axes.

**9. **Find the balance for $
10,000 invested at rate 6.5%
for 8 years,
compounded
**(a) **quarterly
**(b) **continuously.

**10. **Solve: log_{2}**
**x + log_{2}** **(x - 4) = log_{2}** **(x + 24)
.

**11. **Use calculator if necessary to solve for x:
**(a) **
4^{x} 11^{2x - 1} = 19
to four significant places.
**(b) **log
(x - 1) - log (x + 2) =1.

**12.**
**(a) **Given**
**that q is
in quadrant II and sin q
= 2/5 find cos
q .
**(b) **Find
the exact length of the arc intercepted by the central angle q
= 240^{o} in a
circle of diameter 10 feet.

**13. **Let f(x)
= 2 cos(2x - p`/`2 `). `For
this function find its amplitude, period, and phase shift and sketch its
graph on the interval [0,2p].`
`

**14. **The angle of elevation of the
top of a hill from point A on the ground is 25^{o}
. From the point B, 70
feet closer to the hill, the angle of elevation is 30^{o}
.
**(a) **What
is the height of the hill ?
**(b) **What
is the distance from the base of the hill to the point A ?

**15. **Find
the exact value of cos (.a
- b ), given that sin
a = 2/7, and
a be
an angle in quadrant I and cos
b =-1/4, and b
be an angle in quadrant II.

**16. **Find the exact values of
sin (2q),
and cos
(q/2) given
sin q = 5/13,
and q
be an angle in quadrant I.

**17. **Find
the angle between the lines **
**y = x + 4, and **
**y = -2 x + 1.

**18. **Find
all solutions to ** **cos^{2}
x = 1/4 in the interval (0,2p).

**19. **Solve the triangle for
which a = 10, b
= 40^{o} , and
g = 60^{o}
. Find the area of this triangle.

**20. **A surveyor found that two sides
of a triangular lot were 210 ft, and
188 ft, with
an included angle of 75^{o}
. Find the length of third side and the area
of this lot.