Explain what the vertical line test is and how it is used.
What is the range of the given function?
{(–2, 0), (–4, –3), (2, –9), (0, 5), (–5, 7)}
{x | x = –5, –4, –2, 0, 2}
{y | y = –9, –3, 0, 5, 7}
{x | x = –9, –5, –4, –3, –2, 0, 2, 5, 7}
{y | y = –9, –5, –4, –3, –2, 0, 2, 5, 7}
Answers
✧ [tex] \underline{ \underline{ \pink{\large{ \tt{E \: X \: P \: L\: A \: N \: A \: T \: I \: O \: N}}}}}: [/tex]
Part 1 :
☃ [tex] \underline{ \large{ \sf{Vertical \: Line \: Test}}} : [/tex] ⇾ All the relations are not functions. We can determine ( identify ) whether a relation is function or not by drawing a vertical line intersecting the graph of the relation. This is called the vertical line test.
If the vertical line intersects the graph of a relation at one point , the relation is a function.If it cuts at more than one point , it is not a function. It means that if there are more points of the graph of a relation of a vertical line , same first component ( pre - image ) has more images ( second component ) which is not the function by definition.( See the attached picture )
In the picture ' 1 ' , The vertical line ( dotted line ) cuts the graph at one point ( P ). Thus the graph represents a function.In the picture ' 2 ' , The vertical line ( dotted line ) cuts the graph at two points P & Q. So, the graph does not represent a function.Part 2 :
☂ The set of all the images of the elements of domain under the function ' f ' is called the range of a function. In other words , the set of second components of a function is called range. We are given the function :
{(–2, 0), (–4, –3), (2, –9), (0, 5), (–5, 7)}The above numbers [ in bold ] are the range of given function. Now, If we arrange these numbers in ascending order, we get ( -9 , -3 , 0 , 5 , 7 ).
Hence , Choice B [ {y | y = –9, –3, 0, 5, 7} ] is correct.
♕ Hope I helped! ♡
☄ Have a wonderful day / night ! ☼
✎ [tex] \underbrace{ \overbrace{ \mathfrak{Carry \: On \: Learning}}}[/tex] ☥
▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
Sample Response:
The vertical line test is a way to determine if a relation is a function. This test determines if one input has exactly one output on the graph. If any vertical line passes through more than one point on the graph, then the relation is not a function because two different outputs have the same input.
Related Questions
A sweater costs $25. The store marks up the price by 85%. What is the selling price of the sweater?
Answers
A small country emits 130,000 kilotons of carbon dioxide per year. In
a recent global agreement, the country agreed to cut its carbon
emissions by 3.1% per year for the next 10 years. In the first year of the
agreement, the country will keep its emissions at 130,000 kilotons and
the emissions will decrease 3.1% in each successive year. How many
total kilotons of carbon dioxide would the country emit over the course
of the 10 year period, to the nearest whole number?
Answers
Answer:1132858
Step-by-step explanation:
The total carbon dioxide the country emit over the course of the 10 year period would be 1,132,858 kilotons.
What is rate of decrease?
The rate of decrease is a constant amount of deduction from a fixed or primary amount.
Here, the carbon dioxide emits by the country per year is 130,000 kilotons.
The rate of decrease of the carbon dioxide emission per year would be 3.1%.
In the 1st year, the carbon dioxide emission = 130,000 kilotons.
In the 2nd year, the carbon dioxide emission = 130,000 × (100-3.1)/ 100 kilotons = 125,970 kilotons.
In the 3rd year, the carbon dioxide emission = 125,970 × (100-3.1)/ 100 kilotons = 122,064.93 kilotons.
In the 4th year, the carbon dioxide emission = 122,064.93 × (100-3.1)/ 100 kilotons = 118,280.92 kilotons.
In the 5th year, the carbon dioxide emission = 118,280.92 × (100-3.1)/ 100 kilotons = 114,614.21 kilotons.
In the 6th year, the carbon dioxide emission = 114,614.21 × (100-3.1)/ 100 kilotons = 111,061.17 kilotons.
In the 7th year, the carbon dioxide emission = 111,061.17 × (100-3.1)/ 100 kilotons = 107,618.27 kilotons.
In the 8th year, the carbon dioxide emission = 107,618.27 × (100-3.1)/ 100 kilotons = 104,282.1 kilotons.
In the 9th year, the carbon dioxide emission = 104,282.1 × (100-3.1)/ 100 kilotons = 101,049.35 kilotons.
In the 10th year, the carbon dioxide emission = 101,049.35 × (100-3.1)/ 100 kilotons = 97,916.82 kilotons.
Hence, total carbon dioxide emission by that country over 10 years = (130,000 + 125,970 + 122,064.93 + 118,280.92 + 114,614.21 + 111,061.17 + 107,618.27 + 104,282.1 + 101,049.35 + 97,916.82) kilotons = 1,132,857.77 kilotons ≈ 1,132,858 kilotons.
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You are renting a car. You can choose a compact, mid-size,
full-size, or sports utility vehicle. From those
categories you can choose a low, average, or high priced
model. How many different automobile choices do you have?
Answers
Answer:
I believe the answer is 4
Step-by-step explanation:
what is the missing value 4+9=9+?
Answers
Answer:
TᗩKᗴ Tᕼᗴ ᗰIՏՏIᑎᘜ ᐯᗩᒪᑌᗴ ᗩՏ ᙭
[tex]4 + 9 = 9 + x \\ 4 + 9 - 9 = x \\ 4 = x[/tex]
=> ᵗʰᵉ ᵐⁱˢˢⁱⁿᵍ ᵛᵃˡᵘᵉ ⁱˢ 4.
The missing Value is 4.
What is Commutative property?According to the commutative property, the numbers on which we operate can be swapped out or moved without affecting the result. Subtraction and division are not supported by the property, but addition and multiplication are.
Given Expression
4 + 9 = 9 + ?
According to Commutative property
A + B = B + A
for expression
4 + 9 = 9 + 4
or let missing number be x
4 + 9 = 9 + x
x = 4 + 9 - 9
x = 4
Hence the missing value is 4.
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Using the product of the means equals the product of the extremes, solve for x, to the nearest tenth. 4:9=x:6
Answers
Cross multiply:
4 x 6 = 9x
24 = 9x
Divide both sides by 9
X = 24/9
X = 2.7 ( rounded to the nearest tenth)
If p is inversely proportional to the square of q, and p is 25 when q is 3, determine p
when q is equal to 5.
Answers
Answer:
p = 9 when q = 5.
Step-by-step explanation:
p is inversely proportional to the square of q
This means that:
[tex]p = \frac{k}{q^2}[/tex]
In which k is a constant multiplier.
p is 25 when q is 3
We use this to find k.
[tex]p = \frac{k}{q^2}[/tex]
[tex]25 = \frac{k}{3^2}[/tex]
[tex]k = 25*9 = 225[/tex]
So
[tex]p = \frac{225}{q^2}[/tex]
Determine p when q is equal to 5.
[tex]p = \frac{225}{q^2} = \frac{225}{5^2} = 9[/tex]
p = 9 when q = 5.
Sin 0= 8/17 determine the value of tan?
Answers
Answer:
tan theta = 8/15
Step-by-step explanation:
Sin is equal to opposite over hypotenuse. So it means that the side opposite from theta is 8, and the hypotenuse is 17.
To find the value of the adjacent side from theta, use the Pythagorean Theorem.
a^2 + b^2 = c^2
8^2 + b^2 = 17^2
64 + b^2 = 289
Subtract 64.
b^2 = 225
Take the square root.
b = 15.
So that means:
the side opposite from theta is 8,
the side adjacent from theta is 15,
the hypotenuse is 17.
Now we take tan, opposite over adjacent, and use the values from the triangle.
tan = opposite / adjacent
tan = 8/15.
1. Find (f(g(2)) for f(x)= 3x² and g(x)= 5 - x.
Answers
Answer: 27
Step-by-step explanation:
Please help me 7th grade math
Answers
Answer: 1/8
Step-by-step explanation: hoped this helped :))
Suzanne collected data on the weight of her classmates. She found that the range of the data she collected was 17
Which of the following BEST explains what a range of 17 indicates?
A
The average distance of each point from the mean is 17.
.
B
The distance between the minimum and the maximum is 17.
С
The distance between the lower quartile to the upper quartile is 17.
D
The distance between the mean and the median in a skewed data set is 17
Answers
Answer:
the answer is A.
Step-by-step explanation:
A random sample of failure time of 49 kidney transplants (in months) is given: 5.27 43.72 3.96 20.34 44.06 31.18 21.98 34.99 39.36 3.39 23.42 43.41 34.35 46.71 64.87 4.53 7.02 40.50 7.38 37.74 13.49 68.48 48.74 12.85 24.15 27.33 4.82 20.00 55.28 20.83 24.13 11.80 13.82 31.55 36.69 52.57 12.45 40.07 16.86 15.54 15.54 3.85 4.08 5.62 17.44 3.38 41.61 29.52 21.61 If we assume failure time has a Gamma distribution answer the following questions (with 2 decimal points). . Find the critical value for the test (for significance level of 0.1).
Answers
Answer:
Critical value ≈ 1.299
Step-by-step explanation:
number of Kidney transplant ( n ) = 49
Determine the critical value for the test
the sample mean = ∑ failure time / n = 1252.28 / 49 = 25.56
next we determine the standard deviation of the sample
s = [tex]\sqrt{1/(n-1)(xi -X ) ^2}[/tex] = 17.3126
standard error = s / √n = 17.3126 / 7 = 2.4732
Given a significance level of 0.1
df (degree of freedom ) = n -1 = 49 - 1 = 48
∝ = 0.1
critical value = 1.299 ( using excel function ; =T.INV(0.90,48) )
Plz write/type the answers, I pray u can help
Answers
It’ll go the first number is for set one, second number is for set two
Mean: 3, 2.909
Median: 3, 3
Quart: Q1- 2,1
Q2- 3,3
Q3- 4,5
Range: 6,5
SD: 1.73, 1.86
Mode: 3, 1
Hopefully this helps !
How would you write the equation with a slope of 2/3 and a y-intercept of -3 in slope- intercept form
Answers
y=2/3x-2
Explanation:
The equation of a line can be written as y=mx+c
m=slope and c = y-intercept
The point at the x−intercept has coordinates (-3,0)
In y=mx+c
0=2/3(3)+c
0=2+c
-2=c
The equation is y=2/3x-2
Answer:
[tex] y = \frac{2}{3} x - 3[/tex]
Step-by-step explanation:
Slope (m) = 2/3
y-intercept (b) = - 3
Equation of line in slope intercept form is given as:
[tex] y = mx + b[/tex]
Plug the values of m and b in the above equation, we find:
[tex]y = \frac{2}{3} x + ( - 3) \\ \\ y = \frac{2}{3} x - 3[/tex]
If a rectangle has an area of 48 cm², what would be the area of a similar rectangle if
the dimensions are doubled?
A) 2304 cm^2
B) 192 cm^2
C)96 cm^2
D)216 cm^2
Answers
B)192cm^2
Step by step exploration
#9 What is the RADIUS of this circle?
5 cm
Someone plz help my friends ain’t responding
Answers
Answer and Step-by-step explanation:
The radius of this circle is 5 cm.
This is because the radius of any circle is the distance from the middle of the circle to the edge of the circle. The diagram shows us 5cm as that distance.
#teamtrees #PAW (Plant And Water)
NO LINKS OR ELSE YOU'LL BE REPORTED! Please give me the correct answer.Only answer if you're very good at math.
Answers
Answer:
positive
Step-by-step explanation:
hope this helps :)
Answer:
positive
Step-by-step explanation:
because your adding +2 when ur at 0
A passenger must climb 7 steps to a platform to enter the gondola. Each step is 7.5 inches. What would the equation of the ferris wheel circle be on a cartesian coordinate graph if the x-axis is the ground and the y-axis is the axis of symmetry of the ferris wheel.
Answers
Answer:
55
Step-by-step explanation:
The equation of the Ferris wheel circle is [tex](x-0)^{2} +(y - 104.375)^{2} = (100)^{2}[/tex]
What is Ferris wheel?A Ferris wheel is an amusement park ride consisting of a large vertical wheel with places for people to sit or stand spaced evenly around the outer circumference.
What is the standard equation of the circle?The standard equation of the circle is
[tex](x-h)^{2} +(y-k)^{2}= r^{2}[/tex]
Where,
(h, k) is the center of the circle
and, r is the radius of the circle
According to the given question.
The diameter of the Ferris wheel is 200 feet
[tex]\implies radius\ of \ the\ Ferris\ wheel = \frac{200}{2} = 100feet[/tex]
Height of the platform = 7 × 7.5 = 52.5 inches = 4.375 feet
Therefore,
[tex]k = 4.375+100 = 104.375feet[/tex]
and
[tex]h = 0[/tex]
Therefore, the equation of the Ferris wheel circle is
[tex](x-0)^{2} +(y - 104.375)^{2} = (100)^{2}[/tex]
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Farmer Bob can get 10 gallons of milk from 4 cows. How many gallons of milk can he get from 14 cows?
Answers
Answer:
40 gallons of milk
Step-by-step explanation:
trust me that's the answer
The farmer will get 35 gallons of milk from 14 cows.
Process:
1) find the unit rate. do this by taking the independent value and divide it by the dependent value
10/4=2.5
2) Take this number and multiply it by the next dependent value
2.5 x 14 = 35
2. Bart and Jimmy's Ice Cream Shop are designing a new logo for their company. The logo is shown
below. What is the area of Bart and Jimmy's new logo?
A 88.26 cm?
B 74.13 cm
C 58.26 cm
D 44.13 cm
HURRY
Answers
Answer:
Marie Skłodowska-Curie
Polish chemist and pioneer in the field of radioactivity. First woman to become a professor at the University of Paris.
^ po polsku być powinno
Kto Polska?
Brianna measures the temperature of two chemical samples. If the first sample measures -8 degrees Celsius and the second sample measures 24 degrees Celsius, what is the average temperature of the two samples? *
Answers
Answer: + 8 degrees
Step-by-step explanation: average (-8+24)/2= 16/2 degrees
If one side of a cube measures x cm what is the volume
Answers
Answer:
The volume is x times x times x which is x^3 :)
What are some of the applications for exponential functions?
Designing identification tags
Conversion of measurements
Assigning phone numbers
Finding perimeter
Determining the number of subsets in a given set
Answers
Answer:
Option B and D are correct
Step-by-step explanation:
Exponential functions are really useful in the real world situation. They can be used to solve following
a) Population Models
b) Determination of area and perimeters
c) Determine time related things such as half life, time of happening of an event etc.
d) Useful for solving financial problems such as computing investments etc.
Hence, option B and D
Let's say you have a 4 gallon and a 10 gallon pailHow can you measure exactly 2 gallons of water?
Answers
You can fill the 10 gallon pail all the way up. After that, you can pour the water from the 10 gallon pail, into the 4 gallon pail 2 times. That will leave you with 2 gallons in the 10 gallon pail.
Question 9 of 10
True or False? A circle could be circumscribed about the quadrilateral below.
Answers
Answer:
t
Step-by-step explanation:
A circle can be circumscribed about the given quadrilateral, the answer is: A. True.
We know that,
To circumscribe a circle about a quadrilateral means to place the quadrilateral inside the circle, such that the four vertices of the quadrilateral touches the circumference of the circle.
Opposite angles of a circumscribed polygon are supplementary.
Therefore, a circle can be circumscribed about the given quadrilateral, the answer is: A. True.
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14. On Monday, a work group eats at Ava's café,
where a lunch special is $8 and a dessert is
$2. The total is $108. On Friday, the group
eats at Bo's café, where a lunch special Is
$6 and a dessert is $3. The total is $90. Each
time, the group orders the same number of
lunches and the same number of desserts.
How many lunches and desserts are
ordered?
what the x and y value.
Answers
Answer:
no. who eat lunch special = 12
no. who eat dessert = 6
Step-by-step explanation:
Let x = no. who eat lunch special
y = no. who eat dessert
(1) 8x + 2y = 108 (2) 6x + 3y = 90
Divide thru by 2 Divide thru by 3
4x + y = 54 2x + y = 30
-2x - y = -30
2x = 24
x = 12 2(12) + y = 30
24 + y = 30
y = 6
What is the median of 1, 3, 6, 8, 9, 9
Answer choices: A. 6
B. 7
C. 8
D. 9
Answers
Answer:
B
Step-by-step explanation:
The median is the middle value of the data arranged in ascending order. If there is no exact middle value then it is the average of the values either side of the middle.
1, 3, 6, 8, 9, 9
↑ middle
median = [tex]\frac{6+8}{2}[/tex] = [tex]\frac{14}{2}[/tex] = 7 → B
Answer:
B. 7
Step-by-step explanation:
(6 + 8) ÷ 2 = 7
I hope this is right if its not im sorry
Meatball subs used to cost $5.40 at Mike's Sub Shop, but he just increased the price by $0.54.
How much do subs cost now?
Answers
Answer:
Step-by-step explanation: $5.40 + $0.54 now equals $5.94
Which expression is equivalent to 1/5(150x - 80y + 50 - 50x - 25y + 20)?
Answers
Answer:
20x - 21y + 14
1/5(150x - 80y + 50 -50x - 25y + 20)
30x -16y + 10 - 10x - 5y + 4
30x -10x -16y - 5y + 10 + 4
20x -21y + 14
Answer:
20x-21y+14
Step-by-step explanation:
add up like terms and divide them by 5
Determine the amplitude or period as requested. Period of y = - 1/3 * sin 2x
Answers
Answer:
[tex]Period = \pi[/tex]
Step-by-step explanation:
Given
[tex]y = -\frac{1}{3} * \sin(2x)[/tex]
Required
The period
A sine function is represented as:
[tex]y =A \sin(Bx + C) + D[/tex]
Where
[tex]Period = \frac{2\pi}{B}[/tex]
By comparing:
[tex]y =A \sin(Bx + C) + D[/tex] and [tex]y = -\frac{1}{3} * \sin(2x)[/tex]
[tex]B = 2[/tex]
So, we have:
[tex]Period = \frac{2\pi}{2}[/tex]
[tex]Period = \pi[/tex]
Hence, the period of the function is [tex]\pi[/tex]
What is sec 0 when cot 0 = -4/2?
Answers
Answer:
[tex]sec 0=\frac{\sqrt{66} }{8}[/tex]
Step-by-step explanation:
[tex]Cot0=-4\sqrt{2}[/tex]
[tex]sec0=\frac{\sqrt{33} }{4\sqrt{2} }[/tex]
[tex]=\frac{\sqrt{33} }{4\sqrt{4} } *\frac{4\sqrt{2} }{4\sqrt{2} }[/tex]
[tex]=\frac{4\sqrt{66} }{32}[/tex]
[tex]=\frac{\sqrt{66} }{8}[/tex]
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hope it helps...
have a great day!!
