The document contains 20 multiple choice questions about functions. The questions cover topics such as:
- Analyzing graphs of functions and determining function values
- Finding maximums and minimums of functions
- Determining if functions are injective, surjective or inverse functions
- Calculating areas under graphs of functions
A function of two variables is defined similar to a function of one variable. It has a domain (in the plane) and a range. The graph of such a function is a surface in space and we try to sketch some.
A function of two variables is defined similar to a function of one variable. It has a domain (in the plane) and a range. The graph of such a function is a surface in space and we try to sketch some.
MATH 107 FINAL EXAMINATIONMULTIPLE CHOICE1. Deter.docxTatianaMajor22
MATH 107 FINAL EXAMINATION
MULTIPLE CHOICE
1. Determine the domain and range of the piecewise function.
A. Domain [–2, 2];
B. Domain [–1, 1];
C. Domain [–1, 3];
D. Domain [–3/2, –1/2];
2. Solve:
A. 3
B. 3,7
C. 9
D. No solution
3. Determine the interval(s) on which the function is increasing.
A. (−1.3, 1.3)
B. (1, 3)
C. (−∞,−1)and (3,∞)
D. (−2.5, 1)and (4.5,∞)
4. Determine whether the graph of y = 2|x| + 1 is symmetric with respect to the origin,
the x-axis, or the y-axis.
A. symmetric with respect to the origin only
B. symmetric with respect to the x-axis only
C. symmetric with respect to the y-axis only
D. not symmetric with respect to the origin, not symmetric with respect to the x-axis, and
not symmetric with respect to the y-axis
5. Solve, and express the answer in interval notation: | 9 – 7x | ≤ 12.
A. (–∞, –3/7]
B. (–∞, −3/7] ∪ [3, ∞) C. [–3, 3/7]
D. [–3/7, 3]
6. Which of the following represents the graph of 7x + 2y = 14 ?
A. B.
C. D.
7. Write a slope-intercept equation for a line parallel to the line x – 2y = 6 which passes through the point (10, – 4).
A.
B.
C.
D.
8. Which of the following best describes the graph?
A. It is the graph of a function and it is one-to-one.
B. It is the graph of a function and it is not one-to-one.
C. It is not the graph of a function and it is one-to-one.
D. It is not the graph of a function and it is not one-to-one.
9. Express as a single logarithm: log x + log 1 – 6 log (y + 4)
A.
B.
C.
D.
10. Which of the functions corresponds to the graph?
A.
B.
C.
D.
11. Suppose that a function f has exactly one x-intercept.
Which of the following statements MUST be true?
A. f is a linear function.
B. f (x) ≥ 0 for all x in the domain of f.
C. The equation f(x) = 0 has exactly one real-number solution.
D. f is an invertible function.
12. The graph of y = f(x) is shown at the left and the graph of y = g(x) is shown at the right. (No formulas are given.) What is the relationship between g(x) and f(x)?
y = f (x) y = g(x)
A. g(x) = f (x – 3) + 1
B. g(x) = f (x – 1) + 3
C. g(x) = f (x + 3) – 1
D. g(x) = f (x + 1) .
1) Use properties of logarithms to expand the following logarithm.docxdorishigh
1) Use properties of logarithms to expand the following logarithmic expression as much as possible.
Logb (√xy3 / z3)
A. 1/2 logb x - 6 logb y + 3 logb z
B. 1/2 logb x - 9 logb y - 3 logb z
C. 1/2 logb x + 3 logb y + 6 logb z
D. 1/2 logb x + 3 logb y - 3 logb z
2) Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, to two decimal places, for the solution.
2 log x = log 25
A. {12}
B. {5}
C. {-3}
D. {25}
3) Write the following equation in its equivalent logarithmic form.
2-4 = 1/16
A. Log4 1/16 = 64
B. Log2 1/24 = -4
C. Log2 1/16 = -4
D. Log4 1/16 = 54
4) Use properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1.
log2 96 – log2 3
A. 5
B. 7
C. 12
D. 4
5) Use the exponential growth model, A = A0ekt, to show that the time it takes a population to double (to grow from A0 to 2A0 ) is given by t = ln 2/k.
A. A0 = A0ekt; ln = ekt; ln 2 = ln ekt; ln 2 = kt; ln 2/k = t
B. 2A0 = A0e; 2= ekt; ln = ln ekt; ln 2 = kt; ln 2/k = t
C. 2A0 = A0ekt; 2= ekt; ln 2 = ln ekt; ln 2 = kt; ln 2/k = t
D. 2A0 = A0ekt; 2 = ekt; ln 1 = ln ekt; ln 2 = kt; ln 2/k = toe
6) Find the domain of following logarithmic function.
f(x) = log (2 - x)
A. (∞, 4)
B. (∞, -12)
C. (-∞, 2)
D. (-∞, -3)
7) An artifact originally had 16 grams of carbon-14 present. The decay model A = 16e -0.000121t describes the amount of carbon-14 present after t years. How many grams of carbon-14 will be present in 5715 years?
A. Approximately 7 grams
B. Approximately 8 grams
C. Approximately 23 grams
D. Approximately 4 grams
8) Use properties of logarithms to expand the following logarithmic expression as much as possible.
logb (x2 y) / z2
A. 2 logb x + logb y - 2 logb z
B. 4 logb x - logb y - 2 logb z
C. 2 logb x + 2 logb y + 2 logb z
D. logb x - logb y + 2 logb z
9) The exponential function f with base b is defined by f(x) = __________, b > 0 and b ≠ 1. Using interval notation, the domain of this function is __________ and the range is __________.
A. bx; (∞, -∞); (1, ∞)
B. bx; (-∞, -∞); (2, ∞)
C. bx; (-∞, ∞); (0, ∞)
D. bx; (-∞, -∞); (-1, ∞)
10) Approximate the following using a calculator; round your answer to three decimal places.
3√5
A. .765
B. 14297
C. 11.494
D. 11.665
11) Write the following equation in its equivalent exponential form.
4 = log2 16
A. 2 log4 = 16
B. 22 = 4
C. 44 = 256
D. 24 = 16
12) Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents.
31-x = 1/27
A. {2}
B. {-7}
C. {4}
D. {3}
13) Use properties of logarithms to expand the following logarithmic expression as much as possible.
logb (x2y)
A. 2 logy x + logx y
B. 2 logb x + logb y
C. logx - logb y
D. logb x – ...
1. Write an equation in standard form of the parabola that has th.docxKiyokoSlagleis
1.
Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 2x
2
, but with the given point as the vertex (5, 3).
A. f(x) = (2x - 4) + 4
B. f(x) = 2(2x + 8) + 3
C. f(x) = 2(x - 5)
2
+ 3
D. f(x) = 2(x + 3)
2
+ 3
2 of 20
5.0 Points
Find the coordinates of the vertex for the parabola defined by the given quadratic function.
f(x) = 2(x - 3)
2
+ 1
A. (3, 1)
B. (7, 2)
C. (6, 5)
D. (2, 1)
3 of 20
5.0 Points
Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the following rational function.
g(x) = x + 3/x(x + 4)
A. Vertical asymptotes: x = 4, x = 0; holes at 3x
B. Vertical asymptotes: x = -8, x = 0; holes at x + 4
C. Vertical asymptotes: x = -4, x = 0; no holes
D. Vertical asymptotes: x = 5, x = 0; holes at x - 3
4 of 20
5.0 Points
"Y varies directly as the n
th
power of x" can be modeled by the equation:
A. y = kx
n
.
B. y = kx/n.
C. y = kx
*n
.
D. y = kn
x
.
5 of 20
5.0 Points
40 times a number added to the negative square of that number can be expressed as:
A.
A(x) = x
2
+ 20x.
B. A(x) = -x + 30x.
C.
A(x) = -x
2
- 60x.
D.
A(x) = -x
2
+ 40x.
6 of 20
5.0 Points
The graph of f(x) = -x
3
__________ to the left and __________ to the right.
A. rises; falls
B. falls; falls
C. falls; rises
D. falls; falls
Solve the following formula for the specified variable:
V = 1/3 lwh for h
7 of 20
Write an equation that expresses each relationship. Then solve the equation for y.
x varies jointly as y and z
A. x = kz; y = x/k
B. x = kyz; y = x/kz
C. x = kzy; y = x/z
D. x = ky/z; y = x/zk
8 of 20
8 times a number subtracted from the squared of that number can be expressed as:
A. P(x) = x + 7x.
B.P(x) = x
2
- 8x.
C. P(x) = x - x.
P(x) = x
2
+ 10x.
9of 20
Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.
f(x) = x
4
- 9x
2
A. x = 0, x = 3, x = -3; f(x) crosses the x-axis at -3 and 3; f(x) touches the x-axis at 0.
B. x = 1, x = 2, x = 3; f(x) crosses the x-axis at 2 and 3; f(x) crosses the x-axis at 0.
C. x = 0, x = -3, x = 5; f(x) touches the x-axis at -3 and 5; f(x) touches the x-axis at 0.
D. x = 1, x = 2, x = -4; f(x) crosses the x-axis at 2 and -4; f(x) touches the x-axis at 0.
10 of 20
Find the domain of the following rational function.
f(x) = x + 7/x
2
+ 49
A. All real numbers < 69
B. All real numbers > 210
C. All real numbers ≤ 77
D. All real numbers
11 of 20
Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x
2
or g(x) = -3x
2
, but with the given maximum or minimum.
Minimum = 0 at x = 11
A. f(x) = 6(x - 9)
B. f(x) = 3(x - 11)
2
C. f(x) = 4(x + 10)
D. f(x) = 3(x
2
- 15)
2
12 of 20
Solve the following polynomial inequality.
3x
2
+ 10x - 8 ≤ 0
A. [6, 1/3]
B. [-4, 2/3]
C. [-9, 4/5]
D. [8, 2/7]
13 of 20
Find the coordinate.
MODULE 5 QuizQuestion1. Find the domain of the function. E.docxmoirarandell
MODULE 5 Quiz
Question
1.
Find the domain of the function. Express your answer in interval notation.
a.
b.
c.
d.
2.
Indicate whether the graph is the graph of a function.
a. Function
b. Not a function
3.
Graph f(x) = |x – 1|.
a.
b.
c.
d.
4.
Determine whether the function is even, odd, or neither. f(x) = x5 + 4
a. Even
b. Odd
c. Neither
5.
Find the value of f(3) if f(x) = 4x2 + x.
a. 38
b. 39
c. 40
d. 41
6.
Use the graph of the function to estimate: (a) f(–6), (b) f(1), (c) All x such that f(x) = 3
a. (a) 4 (b) 3 (c) –5, 1
b. (a) 5 (b) 4 (c) –3, 1
c. (a) 1 (b) 2 (c) –5, 2
d. (a) 7 (b) 5 (c) –5, 6
7.
The graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g. The graph of is horizontally stretched by a factor of 0.1, reflected in the y axis, and shifted four units to the left.
a.
b.
c.
d.
8.
Evaluate f(–1).
a. –1
b. 8
c. 0
d. –2
9.
Determine whether the function is even, odd, or neither. f(x) = x3 – 10x
a. Even
b. Odd
c. Neither
10.
Indicate whether the graph is the graph of a function.
a. Function
b. Not a function
11.
Determine whether the equation defines a function with independent variable x. If it does, find the domain. If it does not, find a value of x to which there corresponds more than one value of y. x|y| = x + 5
a. A function with domain all real numbers
b. A function with domain all real numbers except 0
c. Not a function: when x = 0, y = ±5
d. Not a function: when x = 1, y = ±6
12.
Graph y = (x – 2)2 + 1
a.
b.
c.
d.
13.
Find the y-intercept(s).
a. –2
b. 1, –3
c. –3
d. None
14.
Determine whether the correspondence defines a function. Let F be the set of all faculty teaching Chemistry 101 at a university, and let S be the set of all students taking that course. Students from set S correspond to their Chemistry 101 instructors.
a. A function
b. Not a function
15.
Determine whether the function is even, odd, or neither. f(x) = –4x2 + 5x + 3
a. Even
b. Odd
c. Neither
16.
Indicate whether the table defines a function.
a. Function
b. Not a function
17.
Use the graph of the function to estimate: (a) f(1), (b) f(–5),and (c) All x such that f(x) = 3
a. (a) –3 (b) –9 (c) 7
b. (a) –3 (b) –9 (c) –1
c. (a) 5 (b) –1 (c) 7
d. (a) 5 (b) –1 (c) –1
18.
Find the intervals over which f is increasing.
a. (–∞, –2], [1, ∞)
b. (–3, ∞)
c. (–∞, –3], [1, ∞)
d. None
19.
Evaluate f(4).
a. 4
b. 10
c. 5
d. –2
20.
Indicate whether the graph is the graph of a function.
a. Function
b. Not a function
21.
Sketch the graph of the function f(x) = –2x + 3.
a.
b.
22.
Find the intervals over which f is decreasing.
a. (–∞, –2), [1, ∞)
b. (–∞, –2], [1, ∞)
c. (–∞, –3), [1, ∞)
d. (–∞, –3], [1, ∞)
23.
Indicate whether the table defines a function.
a. Function
b. Not a function
24.
Indicate whether the graph is the graph of a function.
a. ...
1) Use properties of logarithms to expand the following logarit.docxhirstcruz
1) Use properties of logarithms to expand the following logarithmic expression as much as possible.
Log
b
(√xy
3
/ z
3
)
A. 1/2 log
b
x - 6 log
b
y + 3 log
b
z
B. 1/2 log
b
x - 9 log
b
y - 3 log
b
z
C. 1/2 log
b
x + 3 log
b
y + 6 log
b
z
D. 1/2 log
b
x + 3 log
b
y - 3 log
b
z
2) Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, to two decimal places, for the solution.
2 log x = log 25
A. {12}
B. {5}
C. {-3}
D. {25}
3) Write the following equation in its equivalent logarithmic form.
2
-4
= 1/16
A. Log
4
1/16 = 64
B. Log
2
1/24 = -4
C. Log
2
1/16 = -4
D. Log
4
1/16 = 54
4) Use properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1.
log
2
96 – log
2
3
A. 5
B. 7
C. 12
D. 4
5) Use the exponential growth model, A = A
0
e
kt
, to show that the time it takes a population to double (to grow from A
0
to 2A
0
) is given by t = ln 2/k.
A. A
0
= A
0
e
kt
; ln = e
kt
; ln 2 = ln e
kt
; ln 2 = kt; ln 2/k = t
B. 2A
0
= A
0
e; 2= e
kt
; ln = ln e
kt
; ln 2 = kt; ln 2/k = t
C. 2A
0
= A
0
e
kt
; 2= e
kt
; ln 2 = ln e
kt
; ln 2 = kt; ln 2/k = t
D. 2A
0
= A
0
e
kt
; 2 = e
kt
; ln 1 = ln e
kt
; ln 2 = kt; ln 2/k = t
oe
6) Find the domain of following logarithmic function.
f(x) = log (2 - x)
A. (∞, 4)
B. (∞, -12)
C. (-∞, 2)
D. (-∞, -3)
7) An artifact originally had 16 grams of carbon-14 present. The decay model A = 16e -0.000121t describes the amount of carbon-14 present after t years. How many grams of carbon-14 will be present in 5715 years?
A. Approximately 7 grams
B. Approximately 8 grams
C. Approximately 23 grams
D. Approximately 4 grams
8) Use properties of logarithms to expand the following logarithmic expression as much as possible.
log
b
(x
2
y) / z
2
A. 2 log
b
x + log
b
y - 2 log
b
z
B. 4 log
b
x - log
b
y - 2 log
b
z
C. 2 log
b
x + 2 log
b
y + 2 log
b
z
D. log
b
x - log
b
y + 2 log
b
z
9) The exponential function f with base b is defined by f(x) = __________, b > 0 and b ≠ 1. Using interval notation, the domain of this function is __________ and the range is __________.
A. bx; (∞, -∞); (1, ∞)
B. bx; (-∞, -∞); (2, ∞)
C. bx; (-∞, ∞); (0, ∞)
D. bx; (-∞, -∞); (-1, ∞)
10) Approximate the following using a calculator; round your answer to three decimal places.
3
√5
A. .765
B. 14297
C. 11.494
D. 11.665
11) Write the following equation in its equivalent exponential form.
4 = log
2
16
A. 2 log
4
= 16
B. 2
2
= 4
C. 4
4
= 256
D. 2
4
= 16
12) Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents.
3
1-x
= 1/27
A. {2}
B. {-7}
C. {4}
D. {3}
13) Use properties of logarithms to expand the followin.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
2. FUNÇÕES
1
01. (Espcex 2019) A figura mostra um esboço do gráfico da função x
f(x) a b,
= + com a e b reais, a 0,
a 1
e b 0.
Então, o valor de f(2) f( 2)
− − é igual a
a)
3
.
4
− b)
15
.
4
− c)
1
.
4
− d)
7
.
6
− e)
35
.
6
−
02. (Eear 2019) Considere que o número de células de um embrião, contadas diariamente desde o dia da fecundação
do óvulo até o 30º dia de gestação, forma a sequência: 1
, 2, 4, 8,16,... A função que mostra o número de células,
conforme o número de dias x, é 𝑓: {𝑥 ∈ ℕ; 1 ≤ 𝑥 ≤ 30} → ℕ; 𝑓(𝑥) =
a) x 1
2 −
b) 2x 1
−
c) x
2 1
−
d) 2
x 1
−
03. (Espcex (Aman) 2019) Considere a função 𝑓: ℝ → ℝ definida por 4 2 sen 3x
f(x) ( 3) +
= e a função 𝑔: ℝ → ℝ,
definida por
1 3 cos 2x
3
g(x) .
3
+
=
O produto entre o valor mínimo de f e o valor máximo de g é igual a
a)
1
.
81
b)
1
.
9
c) 1.
d) 9.
e) 81.
04. (Acafe 2019) Considere a função 2
f(x) log x,
= analise as afirmações a seguir e assinale a alternativa correta.
a) Se f(x y) 4
+ = − e 2 2
x y 32
− = então f(x y) 9.
− =
b) f é crescente para x [0, ).
+
c) Existem dois valores x Dom(f)
tais que 2
f(x ) 2.
=
d) A função f é bijetora e sua inversa é definida por 1 1
f (x) .
f(x)
−
=
3. FUNÇÕES
2
05. (Ime 2019) O número de soluções reais da equação
2
2018 (x )
(cos x) 2 2 π
= − , é
a) 0
b) 1
c) 2
d) 3
e) 4
06. (Acafe 2018) Considere as funções f(x) 4
= e 3 2
g(x) x 3x .
= − + Os pontos A e B são as intersecções do gráfico
da função g com o eixo das abscissas. Os pontos G e H são as intersecções dos gráficos das funções f e g. O
quadrilátero de vértices ABGH tem área igual a
a) 6 u.a.
b) 4 u.a.
c) 12 u.a.
d) 18 u.a.
07. (Efomm 2018) Uma aluna do 3º ano da EFOMM, responsável pelas vendas dos produtos da SAMM (Sociedade
Acadêmica da Marinha Mercante), percebeu que, com a venda de uma caneca a R$ 9,00, em média 300 pessoas
compravam, quando colocadas as canecas à venda em um grande evento. Para cada redução de R$ 1
,00 no preço da
caneca, a venda aumentava em 100 unidades. Assim, o preço da caneca, para que a receita seja máxima, será de
a) R$ 8,00.
b) R$ 7,00.
c) R$ 6,00.
d) R$ 5,00.
e) R$ 4,00.
08. (Epcar 2018) De acordo com o senso comum, parece que a juventude tem gosto por aventuras radicais. Os alunos
do CPCAR não fogem dessa condição. Durante as últimas férias, um grupo desses alunos se reuniu para ir a São Paulo
com o objetivo de saltar de “Bungee Jumping” da Ponte Octávio Frias de Oliveira, geralmente chamada de “Ponte
Estaiada”. Em uma publicação na rede social de um desses saltos, eles, querendo impressionar, colocaram algumas
medidas fictícias da aproximação do saltador em relação ao solo. Considere que a trajetória que o saltador descreve
possa ser modelada por uma função polinomial do 2º grau 2
f(x) ax bx c,
= + + cujo eixo das abscissas coincida com a
reta da Av. Nações Unidas e o eixo das ordenadas contenha o “ponto mais próximo da Avenida”, indicados na figura.
Considere, também, as medidas informadas.
O coeficiente de 2
x da função com as características sugeridas é igual a
a)
22
1.521
b)
2
117
c)
13
1.521
d)
13
117
4. FUNÇÕES
3
09. (Epcar 2018) O gráfico a seguir é de uma função polinomial do 1º grau e descreve a velocidade v de um móvel em
função do tempo t :
Assim, no instante t 10
= horas o móvel está a uma velocidade de 55 km h, por exemplo. Sabe-se que é possível
determinar a distância que o móvel percorre calculando a área limitada entre o eixo horizontal t e a semirreta que
representa a velocidade em função do tempo. Desta forma, a área hachurada no gráfico fornece a distância, em km,
percorrida pelo móvel do instante 6 a 10 horas.
É correto afirmar que a distância percorrida pelo móvel, em km, do instante 3 a 9 horas é de
a) 318
b) 306
c) 256
d) 212
10. (Espcex 2018) Na figura estão representados os gráficos das funções reais f (quadrática) e g (modular) definidas
em ℝ. Todas as raízes das funções f e g também estão representadas na figura.
Sendo
f(x)
h(x) ,
g(x)
= assinale a alternativa que apresenta os intervalos onde h assume valores negativos.
a)
3, 1 6, 8
− −
b)
, 3 1
, 6 8,
− − − +
c)
, 2 4,
− +
d)
, 3 1
, 2 7,
− − − +
e)
3, 1 2, 4 6, 8
− −
5. FUNÇÕES
4
11. (Esc. Naval 2018) Seja a função real 𝑓: [2, 4] → ℝ, definida por 2
f(x) 0,5x 4x 10
= − + e o retângulo ABOC, com
A(t, f(t)), B(0, f(t)), O(0, 0) e C(t, 0), onde t [2, 4].
Assinale a opção que corresponde ao menor valor da área o
retângulo ABOC.
a) 8
b)
15
2
c)
200
27
d)
50
9
e)
20
3
12. (Efomm 2018) Seja 𝑓: ℝ ∗→ ℝ uma função tal que f(1) 2
= e f(xy) = −
f(−y)
x
, ∀x, y ∈ ℝ ∗. Então, o valor de
1
f
2
será
a) 5
b) 4
c) 3
d) 2
e) 1
13. (Epcar 2018) Considere a função real
1
f(x) ,
2x 2
=
+
x 1.
− Se
1
f( 2 a) f( a),
5
− + + = − então
a
f 1 f(4 a)
2
− + +
é igual
a
a) 1
b) 0,75
c) 0,5
d) 0,25
14. (Ime 2018) Seja f(x) uma função definida nos conjunto dos números reais, de forma que f(1) 5
= e para qualquer
x pertencente aos números reais f(x 4) f(x) 4
+ + e f(x 1) f(x) 1.
+ + Se g(x) f(x) 2 x,
= + − o valor de g(2017) é
a) 2
b) 6
c) 13
d) 2.021
e) 2.023
15. (Ita 2018) Considere as funções 𝑓, 𝑔: ℝ → ℝ dadas por f(x) ax b
= + e g(x) cx d,
= + com 𝑎, 𝑏, 𝑐, 𝑑 ∈ ℝ, a 0
e
c 0.
Se 1 1 1 1
f g g f ,
− − − −
= então uma relação entre as constantes a, b, c e d é dada por
a) b ad d bc.
+ = +
b) d ba c db.
+ = +
c) a db b cd.
+ = +
d) b ac d ba.
+ = +
e) c da b cd.
+ = +
6. FUNÇÕES
5
16. (Ime 2018) Considere as alternativas:
I. O inverso de um irracional é sempre irracional.
II. Seja a função f : A B
→ e X e Y dois subconjuntos quaisquer de A, então f(X Y) f(X) f(Y).
=
III. Seja a função f : A B
→ e X e Y dois subconjuntos quaisquer de A, então f(X Y) f(X) f(Y).
=
IV. Dados dois conjuntos A e B não vazios, então A B A
= se, e somente se, B A.
Obs.: f(Z) é a imagem de f no domínio Z.
São corretas
a) I, apenas
b) I e III, apenas
c) II e IV, apenas
d) I e IV, apenas
e) II e III, apenas
17. (Acafe 2018) Analise as afirmações a seguir e assinale a alternativa que contém todas as corretas.
I. Se a parábola definida pela função 2
f(x) x mx 9
= + + é tangente ao eixo das abscissas, então, o único valor que pode
assumir é m 6.
=
II. O conjunto f
D R { 3, 3}
= − − é o domínio da função
1
f(x) .
| x | 3
=
−
III. Sejam f, g e f g
+ funções reais. Se f e g são funções injetoras, então, f g
+ também será uma função injetora
IV. Se a função f definida em f : R {2} R {a}
− → − por
x 2
f(x)
2 x
+
=
−
é inversível, então, a 1.
= −
a) I - II - III
b) II - III - IV
c) II - IV
d) I - III
18. (Esc. Naval 2018) Seja 𝑓: ℝ → ℝ. Assinale a opção que apresenta f(x) que torna a inclusão f(A) f(B) f(A B)
verdadeira para todo conjunto A e B, tais que 𝐴, 𝐵 ⊂ ℝ.
a) x
f(x) e cos(x)
=
b) x
f(x) e sen(x)
=
c) x
f(x) 17e
=
d) 3 x
f(x) (x )e
=
e) 2 x
f(x) (x 2x 1)e
= − +
7. FUNÇÕES
6
19. (Espcex 2018) A curva do gráfico abaixo representa a função 4
y log x
=
A área do retângulo ABCD é
a) 12.
b) 6.
c) 3.
d) 4
3
6log .
2
e) 4
log 6.
20. (Epcar 2018) Seja 𝑓: ℝ → ℝ uma função definida por 2
x 3, se x 2
f(x) .
x
x, se x 2
4
−
=
−
Analise as proposições a seguir e
classifique-as em V (VERDADEIRA) ou F (FALSA).
( ) A função f é injetora.
( ) ∀𝑥 ∈ ℝ, a função f é crescente.
( ) A função 1
f−
inversa de f, é dada por 𝑓−1
:ℝ → ℝ, tal que 1 x 3, se x 1
f (x)
4x 4 2, se x 1
− + −
=
+ +
A sequência correta é
a) F – V – V
b) V – V – V
c) F – V – F
d) V – F – V
GABARITO
1 - B 2 - A 3 - D 4 - A 5 - D
6 - C 7 - C 8 - B 9 - A 10 - B
11 - E 12 - B 13 - D 14 - B 15 - A
16 - B 17 - C 18 - C 19 - B 20 - B