Which of the following rational functions is graphed below?
A. F(x) =(x-2)/(x+5)
B. F(x) =1/(x-2)(x + 5)
C. F(x) =1/(2x + 5)
D. F(x)= 1/(x+2)(x-5)
Answers
You can try predicting the graph on some special points and will see it quickly the function which is plotted on the graph.
The rational function which is graphed below is given by
Option D: F(x)= 1/(x+2)(x-5)
How to find the function which was used to make graph?There are many tools we can use to find the information of the relation which was used to form the graph.
A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.
If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.
How to do analysis of the given graph to find the function it represents?Since the graph is almost zero always except x = -2 and x = +5 ( since 5 lines are denoting 10,thus lines on x axis are made on two two intervals), thus the function must be such that as input increases, the output decreases quickly but stays above or below the x axis as per the interval.
The graph goes to +infinity or - infinity(depending on the sign of the function) as the input value x = -2 or + 5, this shows that there can be some value like (x + 2)(x- 5) in the denominator so that as x tends to -2 or +5, the denominator shrinks fast and therefore the function gets immensely big numbers.
I chose them since
[tex](x+2)(x-5)|_{x=-2} \: = (-2+2)(-2-5) = 0 \times -7 = 0\\\\(x+2)(x-5)|_{x=5} \: = (5+2)(5-5) = 7 \times 0 = 0[/tex]
As denominator goes to zero, the function will have big and big values.
We can see that when x < -2, the denominator [tex](x+2)(x-5)[/tex] is positive, and the function tends to upside, and when -2 < x < 5, the function is negative and when 5 < x, the function is positive again.
This shows that the function is having signs just like the denominator.
Thus, out of the options available, the fourth option seems so fit.
Thus,
The rational function which is graphed below is given by
Option D: F(x)= 1/(x+2)(x-5)
Learn more about functions and graphs here:
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Related Questions
Find the distance Between points (3,7) and (-3,4).
Answers
Answer:
the distance is 3√5 !
Step-by-step explanation:
Answer:
Since the points form a triangle, you can use Pythagorean theorem to solve this.
Side A is 3 Units, and side B is 6. The letters do not matter when corresponding them to the sides.
So Pyth Theorem = a^2 + b^2 = c^2
And c^2 is the distance we must find
So a^2 = 9
b^2 = 36
So 36 + 9 = 45
To find C, you must root c^2
So sqrt of 45 is 6.7
The distance between points (3,7) and (-3,4) is 6.7 units.
A pigeon was sitting 15 feet from the base of a telephone pole and flew 25 feet to reach the top of the pole. How tall is the telephone pole?
Answers
Use rulers and compasses to draw a line which is perpendicular to line AB at point C
Answers
Answer:
Draw a line AB
Take a point C on AB
Fix the tip of compass at C and with a fix radius, cut AB on both sides of C
Mark those points D and E
Fix the tip of compass on D, and with the same radius, draw an arc above C
Do the same with E
Those two arcs will intersect at a point, mark the point F
Make a line passing through both C and F
Line CF is perpendicular to AB
pls answer the question important
Answers
Step-by-step explanation:
no they are not parallel
Answer:
not equal
Step-by-step explanation:
its not parallel because sum of angles of alternate angle are not equal.
guys pls answer my question i am very confused
Answers
You’ll have to solve for y:
Start by distributing 5 into (3 + y):
2y = 5(3 + y)
2y = 15 + 5y
Subtract 15 from both sides:
2y - 15 = 15 - 15 + 5y
2y - 15 = 5y
Then, subtract 2y from both sides:
2y - 2y - 15 = 5y -2y
-15 = 3y
Then , divide both sides by 3 to solve for y:
-15/3 = 3y/3
-5 = y
Therefore, y = -5
You’re solving for Y
Lori is solving the equation 4x2 + 5x - 6 = 0 using the quadratic formula. Which
expression shows the correct numbers substituted into the quadratic formula to
solve?
Answers
Answer:
[tex] \frac{ - 5 + \sqrt{( {5})^{2} } - 4(4)( - 6) }{ 2(4)} [/tex]
A book sold 33,100 copies in its first month of release. Suppose this represents 7.8% of the number of copies sold to date. How many copies have been sold to date?
Round your answer to the nearest whole number.
Answers
33100 = .078 x total (change from percent to decimal)
33100/.078 = total (divide both sides by decimal)
424358.9 = total
Round to 424,359 copies.
Which number is larger, 4.7 or 4.7777 77777? Explain your answer.
Answers
Answer:
4.7777 is larger
Step-by-step explanation:
4.7777 can be approximately written as 4.8
4.8 > 4.7
4.7777 > 4.7
Seven plus seven equal to
Answers
Answer:
the answer is 14
Step-by-step explanation:
7+7=14
I hope this help
Answer:
14
Step-by-step explanation:
Work out an expression for the nth term of this sequence. 3, 11, 19, 27, …
Answers
Answer:
8n-5
Step-by-step explanation:
Find the difference between the numbers, +8 so 8n then subtract the diffference from the first number so 3 - 8= -5
The expression will be 8n - 5
Help plz. I will give brainilest!
Answers
Answer:
4.35
Step-by-step explanation:
Make the numerator improper, by doing 8x4+3 which equals 35. And then drag that whole number to the front and slap a decimal between the whole number (4) and your new numerator (35)! Which would be: 4.35
What is the equation of the line that passes through the point (2, 1) and has a
slope of 3/2?
Answers
Given :-
A line having a slope of 3/2 passes through (2,1) .To Find :-
The equation of the line .Answer :-
According to the question ,
m = 3/2 Point = (2,1)We know Point slope form of the line as ,
y - y¡ = m ( x - x ¡ )Substitute ,
y - 1 = 3/2 ( x - 2 ) y - 1 = 3/2x - 3/2*2y - 1 = 3/2x - 3 2( y -1) = 3/2x *2 - 3*22y - 2 = 3x - 6 3x - 2y -4 = 0Hence the equation of the line is 3x -2y-4=0 .
Answer:
Step-by-step explanation:
Use the form y = mx + b and plug in your known point
y = 3x/2 + b
1 = 3(2)/2 + b
1 = 3 + b
b = -2
y = 3x/2 - 2
we can use a plotting calculator to verify our result.
Find the slope of the line that passes through (7,5) and (4, 9)
Answers
Answer:
-4/3
Step-by-step explanation:
(9-5)/(4-7)
4/-3
-4/3
first distribute, then combine like terms 5(2x+7)+4x
Answers
Answer:
14x+35
Step-by-step explanation:
10x+4x=14x
5*7=35
Answer:6x+12
Step-by-step explanation: combine like terms.
Which sentence illustrates the commutative property for addition? (1) (a+b)+c=a+(b+c)
(2) a(b+c)=ab+ac
(3) a+0=a
(4) a+b=b+a
Answers
Answer:
the answer is 2a(b+c)=ab+acAnswer:
The 4th option is correct. a+b = b+a
Step-by-step explanation:
solve pls brainliest
Answers
Answer:
a) -10
b) +150
Answer: (a.) -50/5=-1 (b.) 5*30=+150
Step-by-step explanation:
(a.) each stock went down by -10x5=-50
(b.) 5x10=50. 50x3=150
half way I was doing this it got deleted
Aaron's car used 3- gallons of gas when
he drove it 60 miles. How many miles
does his car get per gallon?
Answers
60 miles/3 gallons = 20 miles/gallon
This is because 60/3=20.
I hope this makes sense.
Answer:
His car gets 20 miles per gallon.
Step-by-step explanation:
1. 60 = 3x (divide by 3)
2. 20 = x
Therefore, the car uses 20 miles per gallon.
Solve This
[tex]6 {}^{2} \times 6 {}^{3} [/tex]
[tex]( \sqrt{103} [/tex]
Answers
Hey there!
Question #1
6^2 × 6^3
6^2
= 6 × 6
= 36
6^3
= 6 × 6 × 6
= 36 × 6
= 216
36 × 216
= 7,776
6^2 × 6^3
= 6^5
• Question #1 answer: 7,776 or 6^5 either answer should work because both answers are equivalent
Question #2
√103
= 10.148892
• Question #2 answer: 10.148892
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Answer:
[tex] \small \sf \: 6 {}^{5} [/tex]
Alternate form: - 7776.
Step-by-step explanation:
1). 6² × 6 ³.
6² = 6 × 6 = 366³ = 6 × 6 × 6 = 2166² × 6³ = 36 × 216 = 7776.
Or,
6² × 6³
= [tex] \sf \small \: 6 {}^{2 + 3} [/tex]= [tex] \small \sf \: 6 {}^{5} [/tex]solve pls brainliest
Answers
Step-by-step explanation:
(a) 46-(-6)= 52
(b) -6+11= 5
please help and give easy to understand explanation.
Answers
Answer:
ok send the work now I am ready
Answer:
I’m not trying to mooch off points, just want to know where the flipping question is
Step-by-step explanation:
Would help if could
Dan has 2 photo albums. Each photo album 8 pages. Dan can fit 4 pictures on each page. How many pictures can Dan fit in the albums?
Answers
Answer:
64
Step-by-step explanation:
8 x 4 = 32
32 x 2 = 64
The number of pictures can Dan fit in the albums are 64.
What is multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
Given that, Dan has 2 photo albums. Each photo album 8 pages. Dan can fit 4 pictures on each page.
Here, the number of pictures
= 2×8×4
= 64
Therefore, the number of pictures can Dan fit in the albums are 64.
Learn more about the multiplication here:
https://brainly.com/question/1562995.
#SPJ2
I really need help someone?
Answers
Answer:
$11.80
Step-by-step explanation:
5x.90=4.5
63.5-4.5=59
59/5=11.8
7.) She offered the Sharks 15% of her company for $30,000. How much is her
company worth? (Hint, Use a proportion to find what 100% of her company is
worth)
% 15
100%
$ 30,000
X
Answers
Answer:
100
Step-by-step explanation: 30/15=2 2*50=100
Is 6 hours correct guys?
Answers
Answer:
yes it 6 hours
Step-by-step explanation:
Answer:
8 hours
Step-by-step explanation:
if the jacket is 32$, then we have to go beyond the graph, and make a function line.
so we can find the slope, how much money does she get per hour?
she gets 4$ per hour, meaning the equation is y=4x
y is the amount of money, x is the amount of hours.
substitute our desired amount of money, 32
32=4x
divide each side by 4 and you get 8
Mason goes to a store an buys an item that costs xx dollars. He has a coupon for 30% off, and then a 7% tax is added to the discounted price. Write an expression in terms of x that represents the total amount that Mason paid at the register.
Answers
THE TOTAL AMOUNT THAT MASON PAID IS 549
A box is formed by cutting congruent squares from the corners. Find the maximum volume of a box made out of a 14 inch by 18 inch cardboard. Find
the lenth of the side of the cut out square. Round to the nearest hundredth place "hint: you may have to change your window in desmos.
Jinches
a. Maximum volume
b. length of side of square: x=
inches
Answers
Answer:
Step-by-step explanation:
V = x(14 - 2x)(18 - 2x)
V = (14x - 2x²)(18 - 2x)
V = (252x - 28x² - 36x² + 4x³)
V = 4x³ - 64x² + 252x
V' = 12x² - 128x + 252
0 = 3x² - 32x + 63
x = (32 ±√(32² - 4(3)(63))) / (2(3)
x = (32 ± √268) / 6
x = 8.06 inches, which we ignore as this would mean we have no material left at all in the 14 inch dimension.
or
x = 2.60488... 2.60 inches
Vmax = 0.60(14 - 2(2.60))(18 - 2(2.60)) = 292.86478... = 292.86 inches³
Please please answer super easy
Answers
Answer:
Step-by-step explanation:
You need y by itself on one side of the equal sign and x and the y intercept on the other side.
4x + 2y = - 12 Subtract 4x from both sides
2y = -4x - 12 Divide by 2
2y/2 = -4x/2 - 12/2
y = -2x - 6
Note: y also must be plus. x can be either plus or minus
m = - 2
b = - 6
What is the constant of proportionality in miles per hour?
a.) 0.85 miles per hour
.85
b. 55 miles per hour
IS112.15
c. 60 miles per hour 4
120
d. 51 miles per hour
15
75
8
Answers
9514 1404 393
Answer:
(d) 51 miles per hour
Step-by-step explanation:
The constant of proportionality can be found by dividing the distance by the time. It is convenient to choose a time that makes this division simple. We choose 30 min = 1/2 hour.
(25.5 mi)/(1/2 h) = 2(25.5) mi/h = 51 mi/h
The constant of proportionality is 51 miles per hour.
3 2/3 +2.3 (theres a bar on top of the 3 in 2.3 ) =
A. 5
B. 5 2/3
C. 6
D. 6 1/3
Answers
cscy-siny=cosy(coty)
Answers
Step-by-step explanation:
[tex]\csc y - \sin y = \dfrac{1}{\sin y} - \sin y[/tex]
[tex]\:\:\:\:\:\:\:\:=\dfrac{1 - \sin^2y}{\sin y}[/tex]
[tex]\:\:\:\:\:\:\:\:= \dfrac{\cos^2y}{\sin y}[/tex]
[tex]\:\:\:\:\:\:\:\:=\cos y \left(\dfrac{\cos y}{\sin y}\right)[/tex]
[tex]\:\:\:\:\:\:\:\:= \cos y \cot y[/tex]