Download Precalculus Fall Semester Final Exam REVIEW (2013-2014)

Name:
Class:
Date:
Precalculus Fall Semester Final Exam REVIEW (2013-2014)
1. Graph the following piece-wise function
f(x)
= { ...r; + 3,
x;;:: 0
-2x-I,
x <0
y
"
8 17
k
x
--oT
.
2. Convert the logarithmic equation to exponential form.
3. Factor the.following expressions
12x2 -x-6
x2 -5x-6
_
ID: A
Name:
__
4. Given that one root is x
3
= 6; use
ID: A
synthetic division to determine the remaining factors.
2
x -3x -16x-12.
5. Find the following values to the Greatest Integer function
[-2.5]
[-i 1
6. Identify the inverse functionj"'
(x) for thefunction of f(x) = 5x - 2
7. Prove whether the following function is even, odd, or neither. Then determine the type of symmetry
8. Determine the maximum number of zeros of the polynomial function and the end behavior.
f(x)
= -3X4
_2x2 +8x+9
2
Name:
ID: A
--------------------9. Find the domain of the function.
I(x) =
,J 3x -
5
10. Find the domain restrictions of the function.
5x
h(x)
= X ( x2-64 )
11. Graph the rational function. Find any vertical and horizontal asymptotes and x and y interceepts ..
x-2
I(x) =x-3
y
<
0
a ~
,
I
x
.
12. Factor 9x3 + 18x2
-
4x - 8 given that x + 2 is one of its factors.
3
Name:
__
ID: A
=
13. Find the horizontal asymptote of the graph off(x)
_l_6 .
x-
14. Solve the following rational equation for "x"
3
x2 + 5x +6
x-I
7
+--=-x+2
x+3
15. Find the vertical asymptote(s), if any, forf(x)
=
2x+2
x -x-6
.
16. Identify the common function type shown in the graph.
-ic : : : : : : ::
.. ,
a.
b.
:tf)
Absolute Value Function
Identity Function
c.
d.
4
Cubic Function
Quadratic Function
Name:
__
ID: A
17. Solve the following rational inequality.
Interval Notation
2x-4
-->5
x+2
18. Determine the intervals on which the function is increasing, decreasing, or constant.
5
x
19. Solve for x.
5
Name:
__
20.
ID: A
Use long division or synthetic division to divide.
(X4 -7x2 -9x-l0)
(x-2)
+-
21. A polynomial of degree 5 whose coefficients are real numbers has the zeros - 3, 2 + i, and (-5 + i.) Identify
the remaining zeros.
a.
b.
3, -2 + i, -5 - i
2 - i, -5 - i
c.
3, -2 + i, 5 + i
d.
-2 + i,5 - i
22. Are the following exponential functions growth or decay?
I(x)
23.
=.! (3y-2
.
3
Graph of the function.
I(x)
= -log3 (x + 2)
y
.
x
'.
I
r-
6
Name:
_
ID: A
24. Graph of the function.
~y
I"
f7
x
25. Identify the polynomial function that has zeros at -2,0, and 5 and matches the graph below.
x
a.
f(x)';" x3
b.
f(x)
-
= _,x3
= _x3
+3x2 -lOx
3x2 -lOx
c.
f(x)
-3x2
d.
f(x) = x3 + 3x2 -lOx
-10~
26. Identify the right-hand and left-hand behavior of the graph of the polynomial function.
f(x)
= -5x
a.
Falls to the left.
Falls to the right.
c.
Rises to the left.
Rises to the right.
b.
Falls to the left.
Rises to the right.
d.
Rises to the left.
Falls to the right.
5
-llx2 +3
7
Name:
_
ID: A
27. Find the value of the expression without using a calculator.
28. If I(x)
29. Find
= 2x + 3 and g(x) = 4x -
(/g )(x)
for I(x)
=
3, find
4
andg(x)
x
(/0
g )(5).
=X4.
30. Find all the real roots of the function.
I(x) = x3 - 3x2
a. 4, -2,-1
b. -4,2, 1
-
6x
+8
c.
d.
4, -2, 1
4,2,-1
.
31. Find the value of x .
Find the direction angle of the vector.
32.
v= (-3,-5)
33. Find component form of initial point (-1,4) and terminal point (-2,0).
34.
Find the magnitude of vector
(8,-2).
35. Ajet is descending east to an airport at a speed of 100 mph at an angle 32° below the horizontal. Find the
component form of the velocity vector for this jet.
8
Name:
__
ID: A
36. List your 10 parent functions we have studied and know these characteristics:
Even/Odd
DomainiRange
Increasing/Decreasing/Constant
End Behavior in Limit Notation
Inflection Points/Concavity
37. Solve the following equation for "x"
-3 + 3e2x+2 = 9
38. Evaluate these basic log expressions:
log.t 16
2
39. Given a rational function, know how to find all of the following:
VA" HA, SA, Holes, x-ints, y-int
,
40. An F-18 Navy hornet jet is flying on course S55°W at a speed of 520 MPH. There is a strong wind
45 MPH blowing in the direction of S65°E. Draw a picture and find the resultant vector magnitude
(speed) and course.
9