Based on the table, which statement best describes a prediction for the end behavior of the graph of f(x)? As x → ∞, f(x) → –∞, and as x → –∞, f(x) → ∞ As x → ∞, f(x) → ∞, and as x → –∞, f(x) → ∞ As x → ∞, f(x) → ∞, and as x → –∞, f(x) → –∞ As x → ∞, f(x) → –∞, and as x → –∞, f(x) → –∞
Answers
Answer: The correct option is B, i.e., "As x → ∞, f(x) → ∞, and as x → –∞, f(x) → ∞".
Explanation:
From the table it is noticed that the first row represents the value of x and the second row represents the value of f(x).
The value of f(x) is 14 at x = -5, after that the value of f(x) is decreased as the value of x increases.
The value of f(x) remains unchanged when the value of x approaches to 0 from 1.
The value of f(x) is -6 at x = 0, after that the value of f(x) is increased as the value of x increases.
From the table it is noticed that as the value of x approaches to positive infinity the value of f(x) is also approaches to positive infinity.
[tex]f(x)\rightarrow\infty \text{ as }x\rightarrow\infty[/tex]
From the table it is noticed that as the value of x approaches negative infinity the value of f(x) is also approaches to positive infinity.
[tex]f(x)\rightarrow\infty \text{ as }x\rightarrow-\infty[/tex]
These statement are shown in second option, therefore the second option is correct.
Answer:
The end behavior of the graph of the function f(x) is:
f(x) → ∞, and as x → –∞, f(x) → ∞ As x → ∞,
Step-by-step explanation:
Based on the table we could observe that the function f(x) is increasing to the left of -1 as well to the right of -1 and it attains the minimum value to be -6.
Hence, it can be predicted that the end behavior of the graph of the function f(x) goes to infinity in the left and also it goes to infinity in the right.
Hence, the statement that best describes the end behavior of the graph of f(x) is:
f(x) → ∞, and as x → –∞, f(x) → ∞ As x → ∞.
Related Questions
Megumi earned a salary of $39,312 last year. How much did she earn per month
Answers
2 months in a year
39312/12 = 3276 per month
Answer:
She earned $ 3,276 per month.
Step-by-step explanation:
We know that,
1 year = 12 months,
Given,
Megumi earned a salary of $39,312 last year
⇒ His salary of one year = $ 39,312
⇒ Salary of 12 months = $ 39,312
[tex]\implies \text{salary of 1 month} = \frac{39312}{12}=\$ 3276[/tex]
Hence, she earned $ 3,276 per month.
A total of
644
tickets were sold for the school play. They were either adult tickets or student tickets. There were
56
fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answers
s = a - 56
a + (a - 56) = 644
2a - 56 = 644
2a = 644 + 56
2a = 700
a = 700/2
a = 350 <=== adult tickets
s = a - 56
s = 350 - 56
s = 294 ...student tickets
Suppose a and b are independent events. if p(a)=0.4 and p(b)=0.1, what is p(a u
b.?
Answers
To find the probability of the union of two independent events, use the formula P(A U B) = P(A) + P(B). In this case, P(A U B) = 0.4 + 0.1 = 0.5.
Explanation:To find the probability of the union of two independent events, we can use the formula:
P(A U B) = P(A) + P(B) - P(A ∩ B)
Since the two events, A and B, are independent, the probability of their intersection, P(A ∩ B), is 0. This is because the occurrence of one event does not affect the occurrence of the other event. Therefore, we have:
P(A U B) = P(A) + P(B)
Substituting the given values, we get:
P(A U B) = 0.4 + 0.1
= 0.5
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Rita borrowed 8000 at a rate of 10.5% compounded monthly assuming she makes no payments how much willshe owe after8 years
Answers
If a person is randomly selected, find the probability that his or her birthday is in May. ignore leap years
Answers
May has 31 days
there are 365 days in a year
31/365 probability someone has a birthday in May
The probability of the event A that represents that the man's birthday is in May is 0.084.
What is probability?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur. Mathematically -
P(A) = n(A)/n(S)
Given is a person who is randomely selected.
Assume that the Event A represents that the man's birthday is in may.
Total number of days in the month of may = n(A) = 31
Total number of days in a year = n(S) = 365
Therefore, the probability that the man's birthday is in may will be -
P(A) = n(A)/n(S)
P(A) = 31/365
P(A) = 0.084
Therefore, the probability of the event A that represents that the man's birthday is in May is 0.084.
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For randomly selected adults, IQ scores are normally distributed with a standard deviation of 15. The scores of 14 randomly selected college students are listed below. Use a 0.10 significance level to test the claim that the standard deviation of IQ scores of college students is less than 15. Round the sample standard deviation to three decimal places. 115 128 107 109 116 124 135 127 115 104 118 126 129 133
Answers
STEP 1: Work out the mean of data set
μ = Sum of values in the set ÷ Number of values in the set
μ = 1686 ÷ 14
μ = 120.4 (rounded to one decimal place)
STEP 2: Subtract the mean from each value in the data set, and then square each answer. The table attached below shows the details of the calculation
STEP 3: Add the answers in STEP 2, then divide by 13.
Note: we divide by 13 instead of 14 because our data set is a sample set.
(∑x₁-μ)/13 = 1253.44÷13 = 96.42
The value obtained in STEP 3 is the variance. To obtain the standard deviation, we square root the variance
s = √96.42 = 9.819 (rounded to three decimal places)
----------------------------------------------------------------------------------------------------------------
We want to test the claim that the standard deviation of IQ scores of college students is less than 15. Putting this in the form of hypotheses we get:
H₀: σ=15
H₁: σ<15
The significance level, α, is 0.10
The degrees of freedom, v, is 14 - 1 = 13
Reading from the Chi² table for α = 0.1 and degree of freedom = 13, we have the critical value ≥19.812
The value of the test statistic is given as [(n-1)²s²] ÷ σ²
We have n = 14, s = 9.819, and σ = 15
test statistic = [(13)²(9.819)²] ÷ 15² = 72.417
72.417 is in the critical region (which is values ≥ 19.812) so the result is significant and H₀ is rejected. The standard deviation of IQ scores of college students is less than 15.
To test if the standard deviation of college students' IQ scores is less than 15, we must calculate the sample standard deviation and then perform a chi-square test for variance. Comparing the test statistic to the chi-square distribution at a 0.10 significance level allows us to accept or reject the null hypothesis.
Explanation:To test the claim that the standard deviation of IQ scores of college students is less than 15, we first need to calculate the sample standard deviation. The scores provided are 115, 128, 107, 109, 116, 124, 135, 127, 115, 104, 118, 126, 129, 133. We find the mean of these scores and then use the formula for sample standard deviation.
Step 1: Calculate the mean of the IQ scores.
Step 2: Find the sum of the squared deviations of each score from the mean.
Step 3: Divide by the number of scores minus one (n-1) to get the variance.
Step 4: Take the square root of the variance to find the sample standard deviation.
Once we have the sample standard deviation, we use the chi-square test for variance since we are testing about the population variance. Under the null hypothesis, we assume that the population standard deviation is 15. At a significance level of 0.10, we compare the test statistic to the corresponding chi-square distribution to determine if we can reject the null hypothesis.
Kholdy enterprises' outstanding bonds mature in 6 years, have a par value of $1,000, and make an annual coupon payment of $60. the market yield on the bond is currently 10%. what is the bond's price?
Answers
Outside diameter of a pipe is five and 7/32 inches the wall of the pipe or 5/32 inches thick find the inside diameter
Answers
5 7/32 = 167/32
5/32 + 5/32 (2 wall thicknesses of the pipe) =10/32
167/32 - 10/32 = 157/32
= 4 29/32
The perimeter of a triangle is 240. Its sides are proportional to 3:4:5. The largest side of the triangle is ?
Answers
3x + 4x + 5x = 240 and solve for x.
which is: 12x = 240
x = 20
The longest side is 5x, so the longest side is 100.
A circular pond is to be surrounded by a gravel path. Use the diagram to find the square feet of gravel needed if we know the pond has a radius of 200 ft and the radius of the whole space is 250 ft?
Answers
A company has a sales revenue of $10,000, cost of goods sold of $4500, and other operating expenses of $1500. what is this company's pre-tax income?
Answers
Choose the point-slope form of the equation below that represents the line that passes through the points (−3, 2) and (2, 1).
A. y + 3 = −5(x − 2)
B. y − 2 = −5(x + 3)
C. y + 3 = −one fifth(x − 2)
D. y − 2 = −one fifth(x + 3)
Answers
[tex]\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\qquad \begin{array}{llll} \textit{plug in the values for } \begin{cases} y_1=2\\ x_1=-3\\ m=\boxed{?} \end{cases} \end{array}\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form}[/tex]
A recipe calls for 1/2 cup of ingredient A for every 1 2/5 cups of ingredient B. You use 4 cups of ingredient A. How many cups of ingredient B do you need?
Answers
(1/2)x = 14/5, so x = 28/5 = 5 3/5 cups.
An object is thrown from an initial height of 0 feet with an initial velocity of 160 feet per second. Solve for when it will return to the ground. Show your work and explain the steps used to solve.
Answers
Hence, we can solve this using rectilinear motion equations.
y = vt + 1/2*a*t^2, where
y is the vertical distance
v is the initial velocity
a is the acceleration due to gravity equal to -32.2 ft/s^2
t is the time of flight
However, it would be impossible to have 0 height. I think there is some typographical error right there. Let's just assume a height of 1000 ft. Substituting the values,
100 = 160*t + 1/2*-32.2*t^2
t = 9.3 seconds
Marty has saved $72. He spent $8 on a video rental. Write a ratio as a fraction in simplest form to represent what portion of his savings he has left.
Answers
Tim count his friends fingers by fives. he counts the fingers on six hands. what number does he say?
Answers
determine the heat energy received per kilogram of steam produced
Answers
Note : this value varies greatly with pressure and temperature.
What percentage of muscle weight would you have if 60 pounds out of 140 pounds is muscle weight?
Answers
all you have to do is divide the muscle weight by the total weight which is...60/140=
ANSWER: about 42.86%
p/100=60/140 multiply both sides by 100
p=6000/140
p=300/7 %
p≈42.86% (to nearest hundredth of a percent)
what is 795840000 in a scientific notation
Answers
=
7.9584 x 10^8
hope it helps
How do i simplify this?
Answers
[tex]\bf \cfrac{(xy^{-3})^{-5}}{(x^{-3}y)^{-6}}\impliedby \textit{first off, distribute the exponent} \\\\\\ \cfrac{x^{1\cdot -5}y^{-3\cdot -5}}{x^{-3\cdot -6}y^{1\cdot -6}}\implies \cfrac{x^{-5}y^{15}}{x^{18}y^{-6}}\implies \cfrac{y^{15}\cdot y^6}{x^{18}\cdot x^5}\implies \cfrac{y^{15+6}}{x^{18+5}}\implies \cfrac{y^{21}}{x^{23}}[/tex]
The ordered pair (a, b) gives the location of point P on the coordinate plane. The value of a is zero and the value of b is not zero. Where could point P be located on the coordinate plane?
Select one or more:
x-axis
Quadrant IV
y-axis
Quadrant I
Quadrant II
Quadrant III
Answers
Answer:
y axis and
Step-by-step explanation:
The point P(a, b) where the value of a is 0, hence point P is located on the y axis.
Coordinate planeThe coordinate plane is a two-dimensional surface formed by two lines known as the horizontal axis (x axis) and the vertical axis (y axis). The origin is the point of intersection of both axis and it serves as a reference point.
A point on the coordinate plane is located using the x and y coordinates.
Given the point P(a, b) where the value of a is 0, hence point P is located on the y axis.
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Match each word from Column A with the correct definition from Column B. Column A Column B 1. impulse 2. muster 3. naught 4. renown 5. vacancy 6. thrifty A. the state of being empty or not filled B. nothing, nonexistence C. to stir up or bring to action D. a sudden stirring to do something E. fame F. careful with money
Answers
2. C
3. B
4. E
5. A
6. F
Answer:
The correct matches are:
1. impulse - a sudden stirring to do something
2. muster - to stir up or bring to action. Like to muster up the courage to speak against the wrong doer.
3. naught - nothing, nonexistence
4. renown - fame ; the condition when you are known or talked about by many people.
5. vacancy - the state of being empty or not filled. Like vacancy for new candidates for a job.
6. thrifty - careful with money . Like a person is thrifty about his own time.
Which polygon has an interior angle sum of 1080°?
Answers
The polygon which has an interior angle sum of 1080° is an Octagon
Interior angles of a PolygonFrom the question, we are to determine which polygon has an interior angle sum of 1080°
To find that, we will determine the number of sides the polygon has.
From the formula for sum of the interior angles in a polygon
Sum of interior angles = (n-2)180°
Where n is the number of sides
Then,
1080° = (n-2) 180°
1080° ÷ 180° = n-2
6 = n-2
n = 6 + 2
n = 8
A polygon with 8 sides is called an Octagon
Hence, the polygon which has an interior angle sum of 1080° is an Octagon
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There are 65 people who want to go on a tea cups ride at an amusement park. There are 10 tea cups that each seat 4 people. How many people need to wait before they get to go on the ride?
Answers
An experiment consist of drawing 1 card from a standard 52 -card deck. Let E be the event that card drawn is a 2. Find P(E').
Answers
that is P(E)+P(E')=1, where E' is "not E".
The event E can happen in 4 ways, because there are four 2's that can be drawn.
P(E)=n(E)/52=4/52=0.08
P(E')=1-P(E)=1-0.08=0.92
Answer: 0.92
Find the point on the line y = 3x + 2 that is closest to the origin.
Answers
the slope of the line y=3x+2 is the coefficient of x, that is 3.
2.
the slope of any line perpendicular to the line y=3x+2, is m, such that:
[tex]3*m=-1[/tex]
so [tex]m= \frac{-1}{3} [/tex]
3.
so any line with equation y=-1/3x+k is perpendicular to y=3x+2.
moreover, the line y=-1/3x (so k=0) is the line passing through the origin
(0, 0) and perpendicular to y=3x+2
4. This means that the closest point of y=3x+2 to the origin is the intersection point of lines y=3x+2 and y=-1/3x
5.
to find this point:
3x+2=(-1/3)x
x(3+1/3)=-2
x(9/3+1/3)=-2
x*10/3=-2
[tex]x= \frac{-2*3}{10} = \frac{-6}{10}=-0.6 [/tex]
thus y is : (-1/3)(-6/10)=0.2
Answer: (-0.6, 0.2)
The point on the line [tex]y=3x+2[/tex] that is closest to the origin is [tex](-0.6, 0.2)[/tex].
Given, [tex]y=3x+2[/tex], whose slope is [tex]3[/tex].
Let [tex]m[/tex] is the slope of the line perpendicular to the above line.
So,
[tex]3\times m=-1\\m=-1/3[/tex]
Then, the general equation of a line perpendicular line will be [tex]y=-1/3x+k[/tex].
So the equation line passing through the origin [tex](0,0)[/tex] and perpendicular to the line [tex]y=3x+2[/tex] is [tex]y=-1/3x[/tex] , [tex](k=0)[/tex].
Then the closest point will be the intersection point of these two lines, i.e.
[tex]3x+2=-1/3x\\9x+6=-x\\10x+6=0\\x=-0.6[/tex]
and
[tex]y=\dfrac{-0.6}{3} \\y=0.2[/tex]
Therefore, the point on the line [tex]y=3x+2[/tex] that is closest to the origin is [tex](-0.6, 0.2)[/tex].
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To avoid distortion of extreme values, a good indicator would be the A. mean. B. weighted-mean. C. mode. D. median
Answers
To avoid distortion of extreme values, a good indicator would be the
B. median.
median
11. Edgar Anderson earns $200 a week plus a 15% commission on all sales over $1,000. If Mr. Anderson's sales for one week are $2,500, what is his gross pay for that week?
Answers
so, what's 15% of 2500? well, is just (15/100) * 2500.
so, add that to his $200 salary, and that's his gross pay.
martin brought 30 shares of microsoft at the close price of $24.53. In a few years, Martin sells all of his shares at $33.71. How much money did martin make?
Answers
9.18*30 = 275.4
Of course, we can't take into account inflation, because nothing is said, I mean that the $24 a few years ago are not the same as today ...
Answer:
Money did martin make = 275.4 $
Step-by-step explanation:
Martin brought 30 shares of Microsoft at the close price of $24.53.
Number of shares = 30
Cost per share = 24.53 $
Total cost = 30 x 24.53 = 735.9 $
Martin sells all of his shares at $33.71
Selling price per share = 33.71 $
Total selling price = 30 x 33.71 = 1011.3 $
Gain for Martin = 1011.3 - 735.9 = 275.4 $
Money did martin make = 275.4 $
x+3menor que 8 qual o resultado
Answers
x+3<8
8-3 =5
X<5
any number less than 5 will work