Download College Algebra Spring 2012 Semester Final Review

College Algebra Spring 2012 Semester Final Review
NAME:
 1 3
1. Write an equation for the line in slope-intercept for that passes through  ,   and is perpendicular to
 4 5
the line 2 x  3 y  1  0
2. If a linear line passes though the points (2, -2) and (0,8), then its equation is…
3. Write an equation of a line parallel to the line
2y  6 x  22 and
has a y-intercept of 7
4. Solve and graph solution on a number line. Write answer in interval notation x  1  2
5. Solve and graph solution on a number line. Write answer in interval notation 3x  4  5
2
6. Solve. 10 z  z  3
2
3
1
3
7. Solve. 3x  5 x  2  0
4
3
2
3
8. Solve. 4 x  65 x  16  0
9. Solve. x 4  13x 2  40  0
10. For the function f, find:
a. Domain
b. Range
c. x-intercepts
d. y-intercept
e. State the value of f (2), f (0), and f (1)
Spring 2012 College Algebra Semester Final Review
11. If f ( x)  3x  4 , then find
f ( x  h)  f ( x )
h
12. If f ( x)  x 2  7 x  2 , then find
f ( x  h)  f ( x )
h
13. Given that f ( x)  x 2  6 and g ( x)  3 x  5 , find ……
A. ( f g )( x)
B. ( g g )( x)
14. Find the domain of f ( x)  2 x  1  x  5 . (Write answer in interval notation.]
15. Find the domain of :
A. f ( x) 
x2  5
8 x 2  3x  2
B. f ( x) 
4x
x  25
2
(interval notation]
16. Solve. Graph on a number line and write answer in interval notation.
A. x 2  2 x  8
B. 5 x 2  2 x  4 x 2  3
C. 6 x 2  x  3  2 x 2  3x  2
GRAPH.
Spring 2012 College Algebra Semester Final Review
17. y  x  2  4
18. y  x  2
Domain:
Domain:
Range:
Range:
Vertex:
x-intercept(s)
x-intercept(s)
y-intercept
y-intercept
19. y    x  2   1
20. y   x  4   2
Domain:
Domain:
Range:
Range:
Vertex:
Vertex:
x-intercept(s)
x-intercept(s)
y-intercept
y-intercept
axis of Symmetry:
axis of symmetry:
2
2
--------------------------------------------------------------------------------------------------------------------------------------21. Given: f ( x)  2( x  3)2 ( x  2)( x  4)
Graph without a graphing calculator
A. What is the leading term?
B. Describe the end behavior of the graph.
C. Find the y-intercept
D. Find the x-intercepts and state their multiplicity.
22. Solve. Graph on a number line. Give answers in interval line.
A.
3x
2
x2
B.
x3 1

x4 2
Spring 2012 College Algebra Semester Final Review
23. Use the Rational Zero Theorem(make a list) , the given graph and synthetic division to find all zeros of
the polynomial function: f ( x)  2 x 4  3x3  x 2  20 x  20 Graph without a graphing calculator
24. Use the Rational Zero Theorem(make a list) , the given graph and synthetic division to find all zeros of
the polynomial function: f ( x)  x5  3x 4  3x3  9 x 2  4 x  12 Graph without a graphing calculator
25. Find and label the intercepts and asymptotes, and then graph the rational function. Show ALL work!
y
3x  7
x  6x  7
2
Vertical asymptote
x-intercept(s)
Horizontal asymptote
y-intercept
26. Find and label the intercepts and asymptotes, and then graph the rational function. Show ALL work!
y
3x  6
x2
Vertical asymptote
x-intercept(s)
Horizontal asymptote
y-intercept
Spring 2012 College Algebra Semester Final Review
27. Given that f ( x)  x 2  9 , find the inverse of f.
28. Graph the function and any asymptotes. State the domain, range and equation of asymptote.
A. y  e x 2  5
B. y  ln( x  2)  4
Domain
Domain
Range
Range
Asymptote
Asymptote
29. Solve for x: 6e2 x  16  8 . Round to 3 decimal places.
30. Solve for x. log3 ( x  9)  log3 ( x  6)  log3 126
31. Solve for x. log5 (4 x  15)  log5 ( x)  2
32. Find the center and radius: x 2  y 2  10 x  8 y  5  0
33. Solve the system of equations.
 x 2  4 y 2  4
A.  2
 x  y  1
2 x  y  6
B. 
 xy  4
 x 2  25 y 2  25
C. 
 x  5 y  1
Spring 2012 College Algebra Semester Final Review
Graph the following. Find the coordinates of the foci and equation of the asymptotes, if any.
34.
x2 y 2

1
4 25
y 2 x2

1
16 49
35.
Foci:
Foci:
Asymptote
36. ( x  3)2  ( y  2)2  5
x2 y 2

1
9 16
37.
Foci:
Center:
Radius:
Asymptote
Find the standard form of the equation of the following graphs.
38.
39.
40.
41.
Spring 2012 College Algebra Semester Final Review