Question 5 of 10
Which of the following rational functions is graphed below?
10 H
10
10
O A. F(x) =
FIX) *-*
X5
X1
B. Fx) = 6-14-5
(x - 1)(x-5)
c. F(X) = 1
D. F(X) = x+5
-
x + 1
Answers
We want to find the equation for the graphed rational function. Notice that the options are not given, so I will try to find the function only from the graph.
The function is:
[tex]f(x) = \frac{(x - 5)}{x - 1}[/tex]
How to analyze the graph of a rational function?The first thing that we can see in the graph is that we have vertical asymptotes at x = 1.
The one in the positive side (of the x range) goes to negative infinity, while the other goes to positive infinity, then the equation will be something like:
[tex]f(x) = \frac{something}{x - 1}[/tex]
Such that the asymptotes are caused when the denominator is equal to zero.
We can see that we also have a horizontal asymptote at y = 1.
This means that, as x tends to infinity, our function will tend to 1, so we have something like:
[tex]f(x) = \frac{(x + b)}{x - 1}[/tex]
The horizontal asymptote is equal to the ratio of the leading coefficients when both polynomials have the same degree, like here, so we can take the two leading coefficients equal to 1, such that:
y = 1/1 = 1
To find the value of b, we evaluate the function in 0:
[tex]f(0) = \frac{b}{-1} = -b[/tex]
And if you look at the graph, you can see that at x = 0 we have:
f(0) = 5
then b = -5
So the function is:
[tex]f(x) = \frac{(x - 5)}{x - 1}[/tex]
If you want to learn more about rational functions, you can read:
https://brainly.com/question/1851758
Related Questions
Solve the following equation for x: 5x-3 1/2 = 9x+4 Enter answers as a decimal with no variable, no spaces, and no equal sign. DO NOT ROUND.
Answers
Answer:
− 1.875
Step-by-step explanation:
Do you want an explanation?
Q1). A={1,2,3} B={2,3,4}. Find (A∩B) xA
Answers
Step-by-step explanation:
Given sets are :
A = {1, 2, 3}
B = {2, 3, 4}
AnB = {1, 2, 3} n { 2,3,4 }
AnB = {2,3}
Now
(AnB) X A
⇛ { 2,3 } X { 1 , 2, 3 }
⇛ { (2,1) , (2,2) , (2,3) , (3,1) , (3,2) , (3,3) }
(AnB) X A for the given problem is
{ (2,1) , (2,2) , (2,3) , (3,1) , (3,2) , (3,3) }
Simplify the expression 2.1(3.7 +5.7u) using the Distributive Property.
PLEASE HELP! :(
Answers
Answer:
7.77+11.97u
Step-by-step explanation:
2.1(3.7+5.7u)=7.77+11.97u
find 66 2/3 of 900
27 1/2% of 1200
17 1/2% of 1000
33 1/2% of 600
Answers
9514 1404 393
Answer:
600330175201 (as written) 200 (if it should be 33 1/3%)Step-by-step explanation:
The easiest way to do these is to make use of your knowledge of the decimal equivalents of fractions and percentages.
66 2/3% of 900 = 2/3 × 900 = 600
27 1/2% of 1200 = 0.275 × 1200 = 330
17 1/2% of 1000 = 0.175 × 1000 = 175 . . . . move the decimal point
33 1/3% of 600 = 1/3 × 600 = 200
or 33 1/2% of 600 = 0.335 × 600 = 201
_____
Additional comment
The repeating decimal for 1/3 is 0.33333.... As a percentage, that is 33 1/3%. Then 2/3 = 66 2/3%.
To change a percentage to a decimal, divide it by 100%.
17.5% = (17.5%)/(100%) = 17.5/100 = 0.175
__
The product 0.275 × 1200 can be rewritten as ...
0.275 × 1200 = 0.275 × 1000 × 1.2 = 275 ×1.2 = 275 + 0.2×275
= 275 +55 = 330
This is a calculation you can do in your head.
__
We suspect a couple of typos in your question. If you mean 66 2/3, not 66 2/3%, then multiply the first answer by 100 to get 60,000.
We have shown answers for both 33 1/2% as your problem says, and 33 1/3%, which would be the more usual fraction.
Assignment Goal:
Describe the motion of a rocket using a quadratic model.
Instructions:
Respond to each of the questions. Your solutions must document all of your work.
Scenario: A toy rocket is launched straight upward from a pad 10 ft above ground level with an initial velocity of 80 ft/sec.
Use the general formula for the vertical position (height) of an object moving under the influence of gravity s=-1/2 gt^2+ v_0 t+ s_0 where s0 is initial vertical position, v0 is initial velocity, and s is vertical position of the object.
1. Define a model (equation) to express the vertical position (height) of the rocket s (in meters) above ground level t seconds after launch. Let g = 32 ft/sec2.
Answers
Answer:
Your question is a little unclear if it wants meters or feet because it has everything listed in nicely feet then you say "(in meters)" at the bottom.
If it wants feet, the answer is
[tex]s=-16t^2+80t+10[/tex]
If it wants meters, the answer is
[tex]s=-4.8768t^2+24.384t+3.048[/tex]
Step-by-step explanation:
To solve, use the quadratic equation.
[tex]y=ax^2+bx+c[/tex]
It wants the x-axis to represent time (t) and the y-axis to represent position (s)
[tex]s=at^2+bt+c[/tex]
It gives us a formula that tells us what a, b, and c equal.
[tex]s=(-1/2)gt^2+v_0t+s_0[/tex] where g is gravity, v_0 is the initial velocity, and s_0 is the initial starting position.
From here, it is just a plug and chug to get the final answer.
[tex]s=(-1/2)(32)t^2+80t+10\\s=-16t^2+80t+10[/tex]
If it wants everything in meters, just convert feet to meters at every step. You can search to find that 1 meter=3.28084 feet.
2x+5y=(-24),3x+y=(-10) solve for using elimination method
Answers
Answer:
x equals -2 and y equals−4
What is the value of m
Answers
35.6 355⅝5555555555555555555545455555555
Determine the ordinary simple interest on a 90-day loan of Php8000 at 8 ½ % interest rate.
Answers
Answer:
$170
Step-by-step explanation:
In order to join a dance class at Dancing’s Lily’s Academy, you must pay a $335 annual fee plus $13.75 for each class you attend. You plan to spend $500 dollars on your dance classes. Write and solve an equation for how many dance classes you will take.
Answers
Answer:
12
Step-by-step explanation:
335 + 13.75x = 500
Subtract 335 from each side
13.75x = 165
Divide each side by 13.75
x = 12
You can attend 12 dance classes with $500.
9514 1404 393
Answer:
12 classes
Step-by-step explanation:
The total cost for c classes will be ...
335 + 13.75c = 500
13.75c = 165 . . . . . . . . . .subtract 335
c = 12 . . . . . . . . . . . divide by 13.75
You will take 12 classes.
I don’t know the answer for this
Answers
Answer:
I think it is probably -12
Step-by-step explanation:
this is really hard help me please
Answers
V = pi(r^2)(h)
r = 3.75, h = 6.21
V = pi(3.75^2)(6.21)
V = pi(87.33)
V = (3.14)(87.33) = around 274
Now you can figure out the rest
NO WORK INCLUDED! JUST ANSWERS!!! PLS HELP
Answers
Answer:
6) = 55
7) = 68
8) = 148
9) = 102
10) = 38
5) = 48
4) =30
3) = 10
2) = 6
1) =4
Hey can anyone help me with these please and thank you !
Answers
Answer:
I would be able to help you but I cant see the work that well. hope you figure it out.
Step-by-step explanation:
Explain how you would use mental math to solve this
proportion.
Answers
You would use mental math by looking at the equation and thinking, “What is 1/75 times 1/2?” Since you want to find out what w is. Since this is mental math, you would know the answer directly, it is 1/150.
Meaning w = 1/150
Is this statement true or false:
a - b = b - a
True
False
Answers
Answer:
False
Step-by-step explanation:
positive A and negative B does not equal positive B and negative A
Answer:
FALSE
Step-by-step explanation:
Find the slope of the line that contains the points (-9, -3) and (-19, -3).
Answers
Answer:
Slope (m) = 0
Step-by-step explanation:
We will use this formula to find the slope⤵⤵⤵
[tex] \frac{y _{2} - y _{1} }{x _{2} - x _{1} } [/tex]
(Sorry if it's a bit small btw)
Now we plug in the values accordingly:
-3 - (-3) = -3 + 3 = 0
-19 - (-9) = -19 + 9 = -10
Slope = 0/-10
So we have 0/-10, which means our slope is actually just 0.
(This also means that the line on the graph will be horizontal.)
Hope this helps you :)
25 + -100 = 25 - n solve the equation mentally
Answers
Answer:
n = 100
Step-by-step explanation:
25 + -100 = 25 - n
=> -100 = -n
=> n = 100
Hoped this helped.
[tex]25-100 = 25 -n\\\\\implies -100 = -n\\\\\implies n = 100[/tex]
Amanda's family is taking a road trip. Their car can travel no more than 352 miles without needing to refill the gas tank. They have
traveled 108 miles since they last filled the gas tank.
Amanda knows that the inequality representing this situation is 108 + x < 352.
Select from the drop-down menu to correctly interpret the solution of this inequality.
Answers
Amanda family cannot travel more than 244 miles without needing to refill the gas tank.
Inequality is the non equal comparison of numbers or variables.
Let x represent the number of miles that they can travel before filling their gas tank.
Their car can travel no more than 352 miles without filling their tank. Also, they have traveled 108 miles since they last filled the gas tank. Hence:
x + 108 < 352
x < 244
This means that Amanda family cannot travel more than 244 miles without needing to refill the gas tank.
Find out more at: https://brainly.com/question/25285332
!PLEASE ANSWER ASAP! THANK YOU!
Sarah’s school awarded 2000 raffle tickets as incentives. The principal will draw one winning ticket. The winner will receive an Ipad mini. Sarah received 4 tickets for good attendance, 5 for making the honor roll, and 10 for tutoring other students.
What is the probability that one of Sarah’s tickets will be selected by the principal? (write your answer as a %, once it is in % form round to the hundredths place)
Answers
Answer
400% Probability Of Sarah Getting Picked !
Step-by-step explanation:
So first 2000 x 19% = 380%
What is the sum of 4 of the interior angles of a regular octagon?
Answers
Answer:
540°
Step-by-step explanation:
inter angle vertex = 135°
135 + 135 + 135 + 135 = 540°
please help i seriously don’t know this at all lol
Answers
Answer:
156m^2
Step-by-step explanation:
label the shapes A and B) triangle=shape b and rectangle=shape a
shape a)10x12=120m^2
shape b)(12x6)/2=36m^2
add the values of shape a and b together to get the area of the shape)120+36=156m^2
PLEASE HELP>>>>>
25 POINTS...................
Answers
Answer:
y = 2/3x - 9
Step-by-step explanation:
note the slope, then note the y intecept, then plug it into the equation y = mx+b
Answer:
So its d
Step-by-step explanation:
Y intercept is 6, and the slope is 3/2. hope i help! And if it isn't that, its c
A suit was marked with a 20% discount.
If the discount is $26.00, what was the original price of the suit?
Answers
Answer:
130
Step-by-step explanation:
Graph the image of this figure after a dilation with a scale factor of 12centered at the origin.
Use the polygon tool to graph the dilated figure.
Answers
Answer:
1.(-4,2)
2.(2,4)
3.(-2,8)
Answer:
(1,2) (0,4) (-4,2)
Step-by-step explanation:
took the quiz and got it right.
The difference of a number and six is negative four
Answers
At football practice on Monday, Brandon threw a football into the target 5 times. The next Monday, he tripled the number of targets he hit. On the following Monday, his hits double that of the week before. Write and evaluate a numerical expression to find how many times he hit the target during those three weeks.
Enter the correct answers in the boxes.
Expression:
Answers
Answer:
try using a different app, it helps with all types of mathematical equations
SectionA
find A and B?
B=
6 9-5
A:
- 10 -4 -8
4 16 6
7
8 4
1 2 -9
19 5 6
9 6
Answers
Answer:
B=24
A= I don't know what that means
Step-by-step explanation:
fast hurry no link no bot please right
Answers
9514 1404 393
Answer:
(d) 972π in³
Step-by-step explanation:
The formula for the volume of a sphere is ...
V = 4/3πr³
The sphere has a diameter of 18 in, so a radius of 9 in. Its volume is ...
V = (4/3)π(9 in)³ = (4/3)729π in³ = 972π in³
The container can hold 972π in³ of water.
There are three compartments for luggage and each compartment has a capacity of 25 pieces of luggage. The first two compartments are full up and the last one contains 8 pieces of luggage. How many pieces of luggage are there?
Answers
Answer:
the first 2 compartments have 25 so 25+25=50, and the last has 8 in it so 50+8=58
PLEASE HELP ME
It snowed 2/3 of a foot in January and 1/2 of a foot in February. How much more did it snow in January than in February?
Answers
Answer:
Step-by-step explanation:
2/3 - 1/2 ?=?
4/6 - 3/6 = 1/6 ft more
