Download Math 1304

Math 1304
Final Exam Review
1. Factor completely.
a.
(6 x  1) 3 (27 x 2  2)  (9 x 3  2 x)(3)(6 x  1) 2 (6)
(6 x  1) 6
1
1
b. ( x 2  4) 2 (3)( 2 x  1) 2 (2)  (2 x  1) 3 (1 / 2)( x 2  4) 2 (2 x)
2. a. Rationalize the numerator.
b. Rationalize the denominator.
x 2
x 2
x 3
x 3
3. a. Write the equation of the perpendicular bisector of the segment whose endpoints are (3,-10) and
(5,11).
b. Write the equation of the line tangent to the circle with center (6,-1) at the point (-2,4).
4. Find the domain. Write in interval form.
f ( x) 
x3
x5
5. Suppose f(x) is given. Describe the following transformations.
a.
b.
c.
d.
e.
y=f(x)+8
y=f(x-2)-2
y=f(-x)
y=1/2f(x)
y=-f(x+3)
Suppose f ( x)  x  1 and g ( x)  x 2  3x . Find:
6. a. f  g (x)
7. a. f
8. a.
1
b. g  f (x)
b. g 1 ( x)
( x)
f ( x  h)  f ( x )
h
b.
g ( x  h)  g ( x )
h
9. Find the zeros and use sign analysis to graph.
p ( x)  3 x 4  2 x 3  x 2
10. Find all asymptotes, holes, intercepts, and graph.
y
x3
x  x  12
2
Solve the following equations.
11. a. 101 x  6 x
b. e 32 x  4
12. a. 2 log x  log 2  log( 3x  4)
b. log 5 x  log 5 ( x  1)  log 5 20
13. a. ln( x  4)  3
b. log x  log( x  3)  1
14. sec x 
3
and x is in quadrant IV. Find all trig functions.
2
15. Find the amplitude, period, phase shift, vertical shift, and graph.
y  3 cos 4( x 

8
)
16. Find exact values.
a. cos 750 
b. tan
5
2
17. Verify the identity.
2(tan x  cot x)
 sin 2 x
tan 2 x  cot 2 x
18. Use the sum and difference formulas to find the exact values.
a. cos 165 
tan 73  tan 13
b.
1  tan 73 tan 13
19. Solve over 0,2 
sin 2x  cos x  0
20. The Great Pyramid of Egypt is 147 meters high, with a square base of sides 230 meters.
Approximate the angle formed when an observer stands at the midpoint of one side and views
the apex of the pyramid.