NO WORK – NO CREDIT Meramec College Algebra TEST 2

Transcription

Meramec
College Algebra
TEST 2 SAMPLE
Fall 2010
NAME:__________________________________Score___________________/100
Please print
SHOW ALL YOUR WORK IN A NEAT AND ORGANIZED FASHION.
Circle T or F, whichever is correct.
NO WORK – NO CREDIT
1. T
F
A zero of a function is a domain element of the function.
2. T
F
A point is on the y-axis if and only if its first coordinate x is zero.
3. T
F
If f(x) = 3x + 2 and g( x ) 
4. T
F
Composition of functions is commutative.
5.
T
F
A zero of a function is a range element.
6. T
F
Every zero of a function is an x-intercept of the graph of the function.
7. T
F
The y-intercept of the graph of a function f is f(0).
8. T
F
The slope of a vertical line is 0.
9. T
F
The slope of a horizontal line is 0.
10. T
F
If the discriminant of a quadratic function is 0, the graph of the function has
one x-intercept.
11. T
F
The graph of a quadratic function is a parabola which opens up if the leading
coefficient is positive and opens down if the leading coefficient is negative.
5
5
, then f  g( x ) 
x
3x  2
12. The vertex of the graph of a quadratic function is (_______, _________).
13. To ask: “Where is f(x) > 0?” is the same as asking: “Where is the graph of f
_________ the _________ axis?”
14. If f and g are functions for which f  g( x )  x and g  f ( x )  x , then f and g are
__________________________ of each other.
15. A function has an inverse if and only if its graph passes the ____________ line test.
16. The point (a, b) is on the graph of the function f if and only if b =_____________ .
17. If the point (4, 9) is on the graph of a function f, then 4 is a ___________ element.
18. If the point (4, 9) is on the graph of a function f, then 9 is a ___________ element.
19. If the point (4, 9) is on the graph of a function f, then f(4) = _________.
h:\mathematics\fall 2010\math 160c test 2 sample fall 2010.docx
1
20. A linear function is a function whose rule may be written in the form ____________.
21. A quadratic function is a function whose rule may be written in the form _________.
22. The squaring function is a function whose rule is _____________.
23. To find the zeros of a function f we must find the real solutions of the equation
resulting from ___________.
24. The y-intercept of the function whose rule is f(x) = 5x3 – 4x2 + 2x + 9 is
_________________.
25. The x-intercepts of the function f whose rule is f(x) = (x + 3)(x + 5)(2x – 5) are
______________________.
26. The discriminant of f(x) = 2x2 – 3x + 4 is _________________________________.
 b
27. The rule for the vertex of the graph of the quadratic function f is 
 2a


, ________ 

28. The graph of a linear function is a _______ _______________ ___________.
In the following multiple choice questions, any number of choices may be
correct. In each question at least one choice is correct. Circle ALL correct
choices.
29.
Consider the function whose rule is f(x) = 3x – 7.
a. f is a linear function
b. The graph of f is a line.
c. The graph of f is a parabola.
d. f(2) = 8.
e. f does not have an inverse.
f. f has an inverse.
30.
Consider the graph shown in Fig. 1.
a. This is the graph of a function.
b. The graph passes the horizontal line test.
c. This is the graph of a quadratic function.
d. This is not the graph of a function.
e. This function has an inverse.
f. This function has at least three real zeros.
31.
In function notation
a. f(x) is the rule of the function.
b. f(x) is a domain element.
c. f(x) is a range element.
d. f is the name of the function.
2
In the following graphing exercises make sure you label the x-intercepts,
y-intercepts, and vertices with their coordinates.
32. Sketch the graph of the function whose rule is f(x) = 2x – 3. Show all computations.
33. Sketch the graph of the function whose rule is
f(x) = x2 – 4x – 5. Show all computations.
34. Sketch the graph of the function whose rule is
f(x) = |x2 – 4x – 5|. No computations required. Use
the previous exercise.
3
35. Consider the graph of f in Fig. 2. Use interval notation to answer Items b, c, and d.
Use the roster method to answer Items a and e.
a. Where is f(x) = 0?
{________________}
b. Where is f(x) < 0?
________________________
c. Where is f(x) > 0?
________________________
d. Where is f decreasing?
_____________________
e. What are the real zeros of f?
{________________}
36. Find the inverse of the function whose rule is f(x) = 5x – 8. Clearly and neatly show
all five steps.
4
a) Law of Trichotomy
b) Transitive Property
c) Distributive Property
d) Definition of function
e) Function notation
f)
g) Definition of zero of a function
h) Zero Factor Property
j)
k) Rule for h
Convention when domain is not specified
Definition of graph
m) Vertical line test
n) Horizontal line test
p) Definition of inverse of a function
q) Definition of linear function
r) Definition of quadratic function
s) Definition of composition
t) Definition of sum of functions
w) Definition of product of functions
MATCHING: For each of the following statements one of the above items is the
justification. Enter the correct letter in the blank preceding each of the
following numbered statements. Some of the above lettered items might get
used more than once and some will not be used.
For this exercise let f, g, and h be functions whose rules are:
f(x) = 4x – 5
g(x ) 
x 5
4
h( x ) 
x2  4
x 5
____ 1) The domain of h is  ,5  5,   .
____ 2) Because f(1) =–1, the point (1, –1) is on the graph of f.
____ 3)
f
 g  (3)  f (3)  g(3)
____ 4) If two functions m and n are inverses of each other, then m  n(4)  4
____ 5) f  g( x )  f  g  x  
____ 6) If two expressions represent the same quantity, the two expressions are equal.
____ 7) Because g 2  
25 7
7
we conclude that g(2) 

4
4
4
5
5
____ 8) f    0 , therefore
is a zero of f.
4
4
(3a  k )2  4
____ 9) h 3a  k  
(3a  k )  5
____ 10) The function whose rule is f(x) = 3x2 – 4x + 9 is a quadratic function.
5
37. Suppose f and g are functions whose rules are f(x) = 3x + 2 and g(x) 
the rule for f  g .
2x
.
x 5
Find
f  g(x) 
38.
Suppose the rule for a function f is f(x) 
2x  1
.
3x2
Calculate the range element associated with –3.
39.
40.
.
Use proper notation. No decimals or mixed numbers.
What is the domain of the function whose rule is f(x) 
3x  2
?
x5
4
3x  2
Show that the point  2,  is on the graph of the function whose rule is f(x) 
7
x5


Use proper notation.
6
41.
Find the rule for the function whose graph is the line through (3, 7) and (–6, 1). No
decimals or mixed numbers.
42. Consider the following facts about a function
named f.
a) f is a quadratic function.
b) The leading coefficient is negative.
c) f(0) = 3
d) f has two zeros – 3 and 1
e) The vertex is (–1,4)
Sketch the graph of f. Label all important points.
7
43.
A ______________ consists of three things;

A set called the ______________

A set called the ______________

A ______________ which associates ______________ element of the
______________ with a ______________ element of the range.
h:\mathematics\fall 2010\math
math 160c test 2 sample fall 2010.docx
8

NO WORK – NO CREDIT Meramec College Algebra TEST 2

Transcription

Similar documents