Do the graphs of all rational functions have at least one asymptote or hole? Explain why or why not

A. No, a function may have neither asymptotes nor holes.

B. Yes, the function will have both a vertical asymptote and hole for any values that cause the denominator to be equal to zero.

C. Yes, the function will have either a vertical asymptote or hole for any values that cause the denominator to be equal to zero

D. Yes, the function will have either a horizontal asymptote or hole for any values that cause the denominator to be equal to zero.​

Answers

Answer 1

Answer:

C. Yes, the function will have either a vertical asymptote or hole for any values that cause the denominator to be equal to zero

Step-by-step explanation:

Answer 2

We want to see if all rational functions always have at least one asymptote or hole.

The answer is C:

" Yes, the function will have either a vertical asymptote or hole for any values that cause the denominator to be equal to zero"

A rational function is something like:

[tex]f(x) = \frac{q(x)}{p(x)}[/tex]

Where q(x) and p(x) are polynomials.

The asymptotes or holes happen when the denominator is equal to zero and the numerator don't.

Now, in the cases where the numerator and denominator become zero for the same value of x, it means that we can factorize the polynomials and remove the common factor. So there we do not have a hole nor asymptote.

Now, because the denominator becomes equal to zero, this means that we are dividing by a reallly small value, then the quotient will tend to infinity or negative infinity, this means that we will have a vertical asymptote.

Then the correct option is C:

Yes, the function will have either a vertical asymptote or hole for any values that cause the denominator to be equal to zero

If you want to learn more, you can read:

https://brainly.com/question/4084552


Related Questions

Which equation represents a line parallel to the line shown on the graph?
A.y = 4 x minus 1
B.y = negative 4 x + three
C.y = one-fourth x + 5
D.y = negative one-fourth x minus 1

Answers

Answer:

c

Step-by-step explanation:

i took the test

can anyone help i don’t know how to do it and it’s GEMDAS not PEMDAS?

Answers

ItS PEMDAS not GEMDAS bro

Answer:

GEMDAS rate. (Abbreviation) A mnemonic used to  the order of operations in math problems; Grouping (such as parentheses), Exponents, Multiplication, Division, Addition, Subtraction.

Step-by-step explanation:

its pemdas just with a different name!!

do you still need help?

Which set of data has the same mode and median?

A. 3, 4, 6, 7, 8
B. 3, 3, 4, 5, 5
C. 6, 7, 7, 8, 9
D. 2, 2, 3, 4, 6

Answers

C both median and mode are 7

Answer:

C

Step-by-step explanation:

the middle number was 7 and so was the most common number

*10 points & it’s due soon*

What is the distance between the points (82) and (7, 6) ?
A 4.1
D 17
23
D) 289

Answers

Sooo just had the same question and the answer is 17

4. What is the sum of trigonometric ratios Cos 16 and Cos 747
A. 0.276
B. 0.961
0.1.237
D. 1.922

Answers

Answer:

I'm not completing sure (maybe a)

Step-by-step explanation:

find measure 6
I’ve tried twice and can’t get it
Geometry

Answers

Measure 6 is equal to 11


Because i dont feel like explaining trust me

Answer:

i think this is the answer

angle 6 = 11

Step-by-step explanation:

Find the slope of the line passing through each of the following pairs of points.
(0, -8), (0,4)

Answers

Answer:

The slope is undefined

Step-by-step explanation:

You can find the slope by doing change in y/change in x.

Y changed by 12 units while x changed by 0.

12/0 is undefined, so the slope is as well (on a graph, the line would be vertical)

0 or undefined or infinity

Step by step explanation:

slope = y2 - y1 / x2 - x1

= 4 + 8 / 0 + 0

= 12 / 0

= 0

The Distributive Property mean to multiply
the number against parenthesis by
everything inside. True or false ?

Answers

Answer:

True.

Step-by-step explanation:

Please help please help

Answers

Pretty sure it is B?

What does x equal to?

Answers

Answer:

Step-by-step explanation:

La X: En matemáticas la x hace referencia a una incógnita o variable. Variable quiere decir que puede tomar un valor específico dentro de conjunto. Por ejemplo, si tenemos "X+1=3" con X que pertenece al conjunto de los números enteros, la X toma el valor exacto de 2 del conjunto de los enteros.

Solve - (7a - 6) = -7a - 2

Answers

Answer:

Hi there

Your answer is

NO SOLUTION!

Step-by-step explanation:

-(7a-6)=-7a-2

-7a+6 = -7a -2

+7a

6=-2

-(7a-6)=-7a-2
-7a+6=-7a-2
statement is then 6=-2
so it’s false meaning there is no solution

Which property was used to write the equation in step 2? Step 1: 5 (x minus 7) = 55. Step 2: 5 x minus 35 = 55. Step 3: 5 x = 90. Step 4: x = 18. distributive property addition property of equality subtraction property of equality division property of equality

Answers

Answer:

distributive property

Step-by-step explanation:

i took the quiz

Answer: It's A

Step-by-step explanation:

How many unit cubes are required to create a larger cube with edge length of 3 units? Can I also get an explanation so I know how it's done? Thanks :)

Answers

Answer:

The unit cubes that are required to create a larger cube with an edge length of 3 units is:

27 cubes.

Step-by-step explanation:

To identify the number of cubes you need to create a larger cube, you must think in the number of cubes of the length (3 cubes in this case), and use the exponent 3, because you need to form a cube. Below I'll show you:

[tex]3^{3}= 27 cubes.[/tex]

To understand it in a better form, suppose that you need a cube with an edge of 5 units, in that case, remember you use the number 5 how base and the exponent is 3, because is a cube, in that case, it would be:

[tex]5^{3}= 125 cubes[/tex]

If it wasn't a cube but a square, you must elevate to the number 2, in the case of the cube is elevated to 3, so, the unit cubes that are required to create a larger cube with an edge length of 3 units is 27 cubes.

William has finished 40 of his 50 problems for math homework. What percent of his homework is finished?

Answers

80 percent is finished

-7-2x=7(x+8)

What is the answer for this expression

Answers

Answer:

x=-7

Step-by-step explanation:

1. Distribute the 7 into the parenthesis: -7-2x=7x+56

2. Combine like terms by doing the opposite operation to the numbers:  -7=9x+56 (added 2x to 7x)

3. Subtract 56 to each side of the equation: -63=9x

4. To isolate the variable "x," divide each side by 9: x=-7

is 6.1 or 6.18 bigger and how you know which one is larger.

Answers

Answer:

  6.18 is larger

Step-by-step explanation:

Written with an equivalent number of decimal places, we are comparing ...

  6.10

  6.18

__

Use these rules for comparison of positive numbers:

1. If the left-most non-zero digits are in number places with different place values, the one with the digit in the highest place value is larger.

2. If the left-most non-zero digits are in number places with the same place value, the number with the larger digit is larger.

3. If the left-most non-zero digits are in the same number place and have the same value, replace those digits with 0, and repeat the comparison starting with the first test above. If one of the numbers has no more non-zero digits, use zero. If both of the numbers have no more digits, they are equal--neither is larger.

__

Following the above rules, we compare the units digits to find they are the same.

Then we compare the tenths digits, and find they are the same.

Then we compare the hundredths digit of 6.18 to 0 to find that 8 > 0, so 6.18 > 6.1

_____

Alternatively (for numbers of any sign), subtract one number from the other. If the result is positive, the minuend is larger. If the result is negative, the subtrahend is larger. If the result is zero. the numbers are equal.

Simplify: 45÷3+2×8-12+42

Show working

Answers

15+2*8-12+42
15+16-12+42
31-12+42
19+42
61

45divided by 3=15

15+2multiplied by 8 -12+42

First multiple 2 and 8=16

15+16-12+42

15+16=31

31-12+42

31-12=19

19+42=61

Answer is61

Which point represents the fraction 7/10?



M
K
J
L

Answers

The answer is M because if you count 1 to 10 on the graph just stop on 7 and its m ;)

A taxi charges a flat rate of $3.00, plus an additional
$0.50 per mile. Carl will only take the taxi home if the cost
is under $10, otherwise he will take a bus. Carl is 15
miles from home. Explain how to write and solve an
inequality to determine if Carl will take the taxi or a bus.

HELP

Answers

Answer:he will take the bus

Step-by-step explanation:

Answer:

Let the variable x be the number of miles. Then the problem can be modeled with the inequality 0.5x + 3 < 10,="" in="" which="">x is the number of miles. To solve, first subtract 3 from each

Step-by-step explanation:

Sample Response!!

Could y’all help me out?

Answers

ok I have no Idea just wanted to tell you your killua profile pic is cute

Can someone please give me the answers thank u !!!

Answers

Answer:

D.

Step-by-step explanation:

I have been doing this in Geometry.

We know perpendicular means opposite recipicoles and opposite slopes.

so.. the slope is 3 to get the y-intercept you do this.

(1, 2) Use the points it gave you and the slope 3 and put it is y=mx + b form

2 = 3(1) + b (I do this because I don't know what b is yet) (b = y-intercept)

2 = 3 + b (subtract 3 on both sides)

-1 = b

The equation is y = 3x - 1

can someone please help me with this question

Answers

Answer: 26322

Step-by-step explanation:

321 x 82

Answer:

26,322 is your answer.

Step-by-step explanation:

"The product" is referring to the answer of two numbers that have been multiplied together. Thus the problem is asking you to find [tex]321*82[/tex].

[tex]321*82=26322[/tex]

Find the domain and the range of the given relation
{(-6, 0), (-1,5), (9, -3), (-3,9)}

Answers

Answer:

domain: {-6, -1, 9, -3}

range: {0, 5, -3, 9}

Step-by-step explanation:

domain is the x-values and range is the y-values

5x-2y=15 solve for y

Answers

Answer:

this should be it

Step-by-step explanation:

Mr. Wong wants to purchase 12 new smoke detectors for his house. Store A sells each smoke detector for $17 and Store B sells each smoke detector for $24. If Mr. Wong purchases all his smoke detectors at Store A, how much less will he spend than if he purchased all the smoke detectors at Store B?

Answers

Answer:

$84

Step-by-step explanation:

so for store A, you would do $17*12 smoke detectors,  Which would give you $204. For store B you would do $24*12 smoke detectors. That is $288. Now all you do is 288-204=84. You would save $84 dollars going to store A

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The amount less spend by buying in store A than in store B is $84

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The number of smoke detectors to be purchased.

= 12

Store A:
Cost of one smoke detector = $17

Cost of 12 smoke detectors.

= 12 x 17

= $204

Store B:

Cost of one smoke detector = $24

Cost of 12 smoke detectors.

= 12 x 24

= $288

Now,

The difference between the cost of 12 smoke detectors from store A to store B.

= $288 - $204

= $84

Thus,

The amount less spend by buying in store A than in store B is $84

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ5

someone helpp
solve the following system of equation ​

Answers

First solve for x by doing 3x+2=-2x-8
Then move the -2x to the left side of the equation so you would add 2x which you would have 5x then subtract 2 to the right side so you would have -10 so then you would have 5x=-10 so x=-2 then plug in -2 to get the y which is -4 so it would be (-2,-4)

I need help with this

Answers

Answer:

Im gonna have to say A.

Step-by-step explanation:

Because if you look at the pair triangles in A. The sides are not equal according to the hash marks.

Solve the equation for a, when b=4 and c=5

[tex]17+2b-4c=4(a-7)-3[/tex]

Answers

The answer to the equation is a=9

A is opposite _________???

Answers

Like BC! Hope this helps :)

Please help legit things only or you get banned thanks!!!!!!!!!!!!!

Answers

Answer:

a

Step-by-step explanation:

this property states a line or shape is always equal to itself

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