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 = 2x2 - 7x - 4. Sketch the graph of this function.
7. Find x-
and all the asymptotes of the function f(x)
= (x2 - 4)/(3x2 + 11x - 4). Sketch
the graph of
8. Find the inverse function of the function f(x) = 2x-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,
(a) quarterly (b) continuously.
10. Solve: log2 x + log2 (x - 4) = log2 (x + 24) .
11. Use calculator if necessary to solve for x:
(a) 4x 112x - 1 = 19 to four significant places.
(b) log (x - 1) - log (x + 2) =1.
(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 = 240o 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 25o
. From the point B, 70
feet closer to the hill, the angle of elevation is 30o
(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 cos2 x = 1/4 in the interval (0,2p).
19. Solve the triangle for which a = 10, b = 40o , and g = 60o . 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 75o
. Find the length of third side and the area
of this lot.