Esmanur Yıldız
Assignment Problem Session 1 due 03/05/2021 at 11:59pm +03
1
Math135 S21
1. (5 points)
Which of the following graphs represent y as a function of x?
Select the letters of the graphs that do represent y as a function of x.
• A. A
• B. B
• C. C
• D. D
• E. E
• F. F
• G. None of the above
2
2. (5 points)
Select all rational functions. There are several correct answers.
• A. r(x) =
5x2 +4x−8
5−3x−5
• B. t(x) =
5−3x3
5x0.7 +4x−8
• C. a(x) =
5x2 +4x−8
5−3x5
• D. b(x) =
• E. s(x) =
5x2 +4x−8
5
√ 2
5x +4x−8
5−3x5
• F. h(x) =
5
5x2 +4x−8
• G. m(x) =
5x+4
5x+4
5x2 +4x−8
5+|x|
√
2
5x +4 x−8
5−3x5
• H. c(x) =
• I. n(x) =
To receive full credit, you must get each checkbox correct.
3
3. (5 points)
Determine whether or not the relation
{(x, 10)| − 8 < x < 1}
is a function and then give its domain and range in interval notation.
(a) Is it a function? [select/yes/no]
(b) Domain:
(c) Range:
4
4. (5 points)
(a) f (0) =
(b) f (−4) =
(c) f (3) =
If f (x) = x2 − 7x, find the following:
5
5. (5 points)
The graph of a function f is shown below.
Use the given graph of f . If there is more than one answer to a question, you can use commas and the word
“or”. When solving an equation for the variable x, your answer should be in the form “x=\ \ \ ”.
a. Evaluate f (−1).
f (−1) =
b. Solve f (x) = 2.
6
6. (5 points)
Find f (15), f (−9), f (π), and f (−9.1) for :
√
f (x) =
x+9
−3
if x > 9
if x ≤ 9
You may keep radicals in any answers where appropriate. Use pi to represent π.
f (15) =
f (−9) =
f (π) =
f (−9.1) =
7
7. (5 points)
Note: this problem has two parts. You will complete the second part after correctly
submitting answers to the following parts (a)-(c).
x
.
Suppose f (x) =
x−1
3
(a) f
=
help (formulas)
t
3
(b) f
=
help (formulas)
t +3
(c) Solve f (x) = 6.
x=
help (numbers)
8
8. (5 points)
This is like the preceding problem except that you must get all answers right before
receiving credit. Let the polynomial p be defined by
p(x) = x3 − 2x2 + 3x + 4
Then p(x − 1) =
x3 −
x2 +
x−
,
Hint: The notation p(x − 1) means ”replace x with x − 1 in the definition of p.
9
9. (5 points)
The graphs of functions f and g are shown below.
Use interval notation in your answers. Use inf to represent infinity.
a. Solve f (x) > g(x)
Solution:
b. Solve f (x) ≤ g(x)
Solution:
10
10. (5 points)
Match the graphs with the corresponding formulas.
?
?
?
?
?
?
1.
2.
3.
4.
5.
6.
f (x) = 1x
f (x) = x
f (x) = 4
f (x) = |x|
f (x) = x12
f (x) = x2
11
A
B
C
D
E
F
12
11. (5 points)
Suppose that g is the function given by the graph below. Use the graph to determine
the values g(−2), g(−1), g(0), g(1), and g(2), if defined. If the function value is not defined, enter DNE
(for ”does not exist”).
g(−2) =
g(−1) =
g(0) =
g(1) =
g(2) =
13
12. (5 points)
A function’s graph is shown below.
Note that the function has a horizontal asymptote and a vertical asymptote.
Use interval notation to answer the following questions. Use upper case letter U to represent the “union”
symbol in set notation.
.
The domain of this function is
The range of this function is
.
14
13. (5 points)
Find the domain and range for the function
(
3x − 8, if x ≤ 2,
f (x) =
7 − 12 x, if x > 2.
Domain:
Range:
Use interval notation.
15
14. (5 points)
Given the graph of y = f (x) below, answer all of the following questions.
(a) Determine f (−5):
(b) Determine f (−10) :
(c) Domain:
(d) Range:
16
15. (5 points)
True or False: [Choose/True/False] If f (x) =
x2 − 25
and g(x) = x + 5, then the
x−5
functions f and g are equal.
In the answer box below, explain your reasoning for the choice of true or false you made above. Use
complete sentences and correct grammar, spelling, and punctuation. Be specific and detailed. Write as if
you were explaining the answer to someone else in class.
17
16. (5 points)
The graph of a piecewise function, f (x), is depicted above. Find its equation:
f (x) =
for
for x [select/<=/<]
[select/<=/<] x [select/<=/<]
for x [select/>=/>]
18
17. (5 points)
f (x)
g(x)
Use the figures above, which show the functions f (x) and g(x), to find the following values. Note that you
can find exact values.
1. f (g(10))=
2. g( f (−1))=
3. g(g(−4))=
19
18. (5 points)
domains.
Let f (x) =
√
x + 1 and g(x) = 2x − 2. Find f ◦ g and g ◦ f , and their respective
1. ( f ◦ g)(x) =
2. What is the domain of f ◦ g ?
Answer (in interval notation):
3. (g ◦ f )(x) =
4. What is the domain of g ◦ f ?
Answer (in interval notation):
20
19. (5 points)
Suppose that f (x) = −5x2 − 5x + 3 and
x<2
5x − 2
−5
2≤x<8 .
g(x) =
x−8
x≥8
Find the following:
(a) ( f ◦ g)(3) =
(b) (g ◦ f )(−2) =
21
20. (5 points)
Use the table of values below for the functions f (x) and g(x) in order to complete the
table of values for the function defined in each part.
x
-1 0 1 2 3 4
f (x) -1 3 7 11 15 19
g(x) 4 1 0 1 4 9
(a) Complete the table for h(x) = f (x) + g(x)
x
h(x)
-1
0
1
2
3
4
0
1
2
3
4
-1
0
1
2
3
4
-1
0
1
2
3
4
(b) Complete the table for j(x) = 3 f (x)
x
j(x)
-1
(c) Complete the table for k(x) = (g(x))2
x
k(x)
(d) Complete the table for m(x) =
g(x)
f (x)
x
m(x)
Generated by ©WeBWorK, http://webwork.maa.org, Mathematical Association of America
22
