Write a rational function for the given scenario. There may be more than one correct answer.

Question 1. X-intercept: none
Vertical Asymptote: X = -3
Horizontal Asymptote: y = 0

Question 2. X-intercept: none
Vertical Asymptote X=2 & x= -2
Horizontal Asymptote: y = 0

Question 3 x-intercept: (3,0) & (-3,0) Vertical Asymptote: X=-1 & x= -4
Horizontal Asymptote: y = 1

Question 4. X-intercept: (-2, 0)
Vertical Asymptote: X = 4 & x=-5 Horizontal Asymptote: y=0

Need to make a rational function for each question.

Answers

Answer 1

Answer:

Q1:     [tex]\frac{1}{x+3}[/tex]

Q2:     [tex]\frac{1}{(x-2)(x+2)}[/tex]

Q3:     [tex]\frac{(x-3)(x+3)}{(x+1)(x+4)}[/tex]

Q4:     [tex]\frac{x(x+2)}{(x-4)^{2}(x+5) }[/tex]

Step-by-step explanation:

If there is a vertical asymptote at x=k, then the denominator must contain a term (x-k) or (x-k) raised to a positive integer power.

If there is an x intercept at k, then the numerator must contain a term (x-k) or (x-k) raised to a positive integer power.

If there is a horizontal asymptote of 0, then the highest power of x in the denominator must exceed the highest power of x in the numerator.

If thee is a horizontal asymptote of k, then the highest power of x in the numerator and denominator must be the same and the ratio of their coefficients (numerator to denominator) must be k.


Related Questions

HELPPPP PLEASE

1. (28 - 22 ) ÷ ( 17-5)

2. (11 x 2 - 42 ) +4

Answers

Answer:

1) 1/2 2) -16

Step-by-step explanation:

28-22=6

17-5=12

--------------

6/12=1/2

------------

2) (11*2-42)+4=(22-42)+4=-20+4=-16

Answer:

1. 0.5 or 1/2

2.-16

Step-by-step explanation:

frecuencia del alcohol​

Answers

????
Dnbdusbsjeisbsbdbbd

Find the area of the rectangle.. Single choice.

436 cm squared
399 cm squared
380 cm squared
417 cm squared

Answers

Answer:

399 cm squared.....Do you want explanation ??

Answer:

socratic

Step-by-step explanation:

use socratic take a pic then it searchers for you

Simplify the expression. Make sure all final answers are clearly labeled. Show all work.

3 divided by 2+√5

Answers

Answer:2 1/3

Step-by-step explanation:2+5=7 3 divided by 7 equals 2 1/3


[tex] - \frac{2}{3} + 4 \times \frac{1}{3} [/tex]

Answers

Answer:

2/3

Step-by-step explanation:

You first multiply 4x1/3 which equals 4/3. Now you do -2/3+4/3=2/3. Hope this helps!

Answer:

2/3

Step-by-step explanation:

[tex]\frac{-2}{3}+4*\frac{1}{3}=\frac{-2}{3}+\frac{4}{3}\\\\=\frac{(-2) + 4}{3}\\\\\\= \frac{2}{3}[/tex]

Please Help me! ASAP

Answers

Your answer would be 44

HELP I PROMISE I WILL GIVE BRAINLIEST!!!!!!!!

Answers

Answer: i think d sorry if im wrong.

Step-by-step explanation:

What is the solution to the system of equations?

Answers

Answer:

(3, -2)

Step-by-step explanation:

both of the equations are equal to y, which means they are equal to each other.

So you write them as equation(1) = equation(2)

and solve for x.

Next substitute the value of x to any of the equations and find y. And that is how I got (3 , -2)

Hope I was able to help:)

ILL GIVE 50 POINTS

Which set of statements explains how to plot a point at the location (Negative 3 and one-half, negative 2)?
Start at the origin. Move 3 and one-half units right because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between 3 and 4. Move 2 units down because the y-coordinate is -2.
Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units left because the y-coordinate is -2.
Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units right because the y-coordinate is -2.
Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.

Answers

Answer:

Option 3 is right

Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units right because the y-coordinate is -2.

Hope this helps:)

It is B from my point of view

ax + 7 = 2x + b
Find x

Answers

Answer:

x = [tex]\frac{b-7}{a-2}[/tex]

Step-by-step explanation:

Given

ax + 7 = 2x + b ( subtract 2x from both sides )

ax - 2x + 7 = b ( subtract 7 from both sides )

ax - 2x = b - 7 ← factor out x from each term on the left side

x(a - 2) = b - 7 ← divide both sides by (a - 2)

x = [tex]\frac{b-7}{a-2}[/tex]

How long does it take an account with a principal of $400 to earn $48 in interest at a simple annual interest rate of 2%?

Answers

Answer:

it'll take 6 years

Step-by-step explanation:

I =put

48= 400(.02) t

48= 8t

t= 6 years

Please help me 2x+y=2

Answers

Answer:

y=-2x+2

Step-by-step explanation:

Inverse of -2x+2 {x-2}{2}

Find the unit rate.
1/2 pound : 5 days

Answers

Answer:

= 0.2 pound per day

Step-by-step explanation:

This is a fraction equal to

1 pound ÷ 5 days

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 5

1 pound ÷ 5

5 days ÷ 5

=  

0.2 pound

1 day

=  

0.2 pound

day

= 0.2 pound per day

The price of a flight was increased by 3% to £720. What was the price before the increase?
Give your answer to the nearest penny.

Answers

699.03 dollars

hope it helps

Which does NOT represent the quotient of 17 ÷ 10? A. 1 7/10 B. 1 R7 C. 10/17 D. 1.7

Answers

Answer:

The answer is C

Step-by-step explanation:

Answer:

C. 10/17

Step-by-step explanation:

10/17 is less than the correct answer 1.7 so it is C.

During the American Revolution, women... i need help now please i will give 11 points


1.ran family businesses.

2.cared for the troops.

3.helped raise money for the war.

4.all of the above

Answers

Answer:

its 4 or d

Step-by-step explanation:

hope this helps!

please mark me brainliest! thanks!

solve (x - 4)^2 = 5 ​

Answers

Answer

If you are solving for X, take the root from both sides.

Exact Form:

x

=

5

+

4

,

5

+

4

Decimal Form:

x

=

6.23606797

,

1.76393202

Answer:

Step-by-step explanation:

[tex](x-4)^2=5\\ \\ x-4=\pm \sqrt{5}\\ \\ x=4\pm \sqrt{5}\\ \\ x=4-\sqrt{5},\ 4+\sqrt{5} [/tex]

2. Write the symbol that will make the statement true; -5__+3.
a. < b. > c. = d. /​

Answers

Answer:

a

Step-by-step explanation:

On the number line, negative numbers are less than zero. positive numbers are larger than zero.

At the fair concession stand, a drink costs $1.50, and a hot dog costs $2.75. If Jacob has $18 to spend on food, how many of each item can he buy?
3 drinks and 7 hot dogs
3 drinks and 5 hot dogs
2 drinks and 7 hot dogs
2 drinks and 5 hot dogs

Answers

Answer:

Answer is D (2 drinks and 5 hotdog's)

Step-by-step explanation: 1st answer is over as it is $19.25 for only the hotdogs. 2nd is $18.50 which is a little over. 3rd one is $22.25. And the forth one is $16.75 which is perfect because he cant buy anything else with the remainder of his money.

You can use trial and error for 3 drinks and 2 drinks and can see how many hot dogs are available for Jacob to buy in $18 budget.

Jacob, with $18 dollars for food, under given conditions, can buy:

Option D: 2 drinks and 5 hot dogs.

How to decide what amount of drinks and hot dogs are obtainable in given $18 budget?

This can be modeled by mathematical expression with use of variables, and inequality.

Suppose that you can by [tex]x[/tex] drinks and [tex]y[/tex] hot dogs, then their amount should not exceed $18 and they should try to use that $18 as much as they can.

Since 1 drink costs $1.5 and 1 hot dog costs $2.75, thus,

[tex]1.5x + 2.75y \leq18[/tex]

Using trial and error for 2 and 3 drinks (we could've done fro 5 or 7 hot dogs too)

For 2 drinks:

Since x = amount of drinks = 2, thus from the obtained inequality, we have:

[tex]1.5x + 2.75y \leq 18\\1.5 \times 2 + 2.75y \leq 18\\2.75y \leq 18 - 3\\y \leq \dfrac{15}{2.75}\\\\y \leq 5.555...\\y = 5[/tex]

We took y = 5 since it is closest integer less than 5.55... since we cannot buy drink or hot dog in decimal points generally and cannot spend more than $18

Thus, if Jacob buys 2 drinks, then he can by 5 hot dogs at max.

For 3 drinks:

Since drinks' amount increased, then hot dogs amount will have to decrease to keep them together under $18. And since in 2 drinks Jacob could by 5 hot dogs, thus, now he will have to buy less than 5 hot dogs, which are not given in options.

Thus,

Jacob, with $18 dollars for food, under given conditions, can buy:

Option D: 2 drinks and 5 hot dogs.

Learn more about inequalities here:

https://brainly.com/question/11901702

Your cat is 8 years younger than your friend. In 4 years, your friend will be twice as old as your cat. How old is your cat now?
years old

Answers

Answer:

your  cat will be 12 your friend will be either 16 or 24

Step-by-step explanation:

Friend is 12 years old and cat is 4 years old.

What is equation?

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side.

Given,

Cat is 8 years younger than your friend

Let age of friend be x

then, age of cat be x - 8

But In 4 years, your friend will be twice as old as your cat

x + 4 = 2(x - 8 + 4)

x + 4 = 2x - 16 + 8

x + 4 = 2x - 8

-2x + x = - 12

x = 12

Age of friend = 12 years

Age of cat = 12 - 8 = 4 years

Hence, 12 years is age of friend and 8 years is age of cat.

Learn more about equation here:

https://brainly.com/question/1529522

#SPJ5

A new health drink has 150% of the recommended daily allowance (RDA) for a certain vitamin. The
RDA for this vitamin is 20 mg. How many milligrams of the vitamin are in the drink?
There are mg of the vitamin in the drink.

Answers

Convert 150% to a decimal by dividing by 100, = 1.5

Multiply 1.5 times the 20 mg = 30 mg in the drink.

150% is one and a half times a value.

Is my answer right? if not can you please tell me which won is right..

Answers

A = 4 is the correct answer!3 x ? = 1212 ÷ 3 = 4so1 x 4 = 4You're wrong. It is not six.By the way, it's "one" not "won".It was probably a mistake.:)Please let me know if I am wrong.

Which one of these math problems is correct?
A. 50x3=1043
B. 54x6=324
C. 25x4=100
D. None of the above

Answers

Answer:

B and C are correct

Step-by-step explanation:

Use a calculator next time.

Need to figure out x and y

Answers

Answer:

f(X)=7 X=1

X=2. f(X)=14

f(X)=21. X= 3

X=4. f(X)=28

X=5. f(X)=35

just substitute in the equation

$26,000 is invested at 8% p.a. If interest is compounded annually, find the balance after 35 years.​

Answers

Answer:

At the end of 35 years, your savings will have grown to $384,418.

You will have earned in $358,418 in interest.

Estefania can run 3/4 of a race in 2/3 hour. How long will it take her to complete the entire race?

Answers

Answer:

3/4 x = 2/3

If we multiply both sides by 4/3 we will have

x = 2/3 × 4/3 = 8/9 hour

write the equation of the line passing through the points (-4 -1) and (2 8)

Answers

Answer:

y=3/2x+5

Step-by-step explanation:

4x^2-4x+1 factoring special cases

Answers

Answer:

(2x−1)(2x−1)

Step-by-step explanation:

Factor 4x2−4x+1

4x2−4x+1

=(2x−1)(2x−1)

−3(5x + 8) − 7(5x + 3)

Answers

Answer:

-50x-45

Step-by-step explanation:

-3(5x+8)-7(5x+3)

-15x-24-35x-21

-50x-45


Math problem I need help with

Answers

Answer:

31° is the answer thank you

31 degrees Hopefully that helps!
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