Use the drawing tools to sketch the graph of a rational function with a domain of { x | x ∈ R , x ≠ - 5 , 4 } . Include one removable discontinuity and one nonremovable discontinuity. Label each discontinuity using the text tool.

Answers

Answer 1

If [tex]f(x)[/tex] has a removable discontinuity at [tex]x=a[/tex], then the limit

[tex]\displaystyle \lim_{x\to a} \frac{f(x)}{x-a}[/tex]

exists and is finite.

A non-removable discontinuity at [tex]x=b[/tex] would entail a non-finite limit,

[tex]\displaystyle \lim_{x\to b} \frac{f(x)}{x-b} = \pm\infty[/tex]

or the limit does not exist (which could be due to the limits from either side of [tex]x=b[/tex] not matching or existing).

For a rational function, we want

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

where [tex]p[/tex] and [tex]q[/tex] are polynomials in [tex]x[/tex]. To get a removable discontinuity at [tex]x=a[/tex], both [tex]p[/tex] and [tex]q[/tex] must be divisible by [tex]x-a[/tex], and the limit of their quotient after removing these factors still exists. That is,

[tex]\displaystyle \lim_{x\to a} f(x) = \lim_{x\to a} \frac{p(x)}{q(x)} = \lim_{x\to a} \frac{(x-a)p^*(x)}{(x-a)q^*(x)} = \lim_{x\to a} \frac{p^*(x)}{q^*(x)} = \frac{p^*(a)}{q^*(a)}[/tex]

On the flip side, we get a non-removable discontinuity [tex]x=b[/tex] if [tex]p[/tex] is not divisible by [tex]x-b[/tex], in which case

[tex]\displaystyle \lim_{x\to b} f(x) = \lim_{x\to b} \frac{p(x)}{q(x)} = \lim_{x\to b} \frac{p(x)}{(x-b)q^*(x)} = \frac{p(b)}{0\times q^*(b)}[/tex]

and this is undefined.

Suppose [tex]f(x)[/tex] has a non-removable discontinuity at [tex]x=-5[/tex] and a removable one at [tex]x=4[/tex]. Then one such function could be

[tex]f(x) = \dfrac{x-4}{(x-4)(x+5)} = \dfrac{x-4}{x^2+x-20}[/tex]

Related Questions

Encontrar los valores de x,y,z

Answers

The value of the angles x,y, and z is 73 degrees,88 degrees, and 55 degrees.

We have given that,

Two overlapping triangles

Here we have the angle Z and 52

What is the sum of the angle in a triangle?

The sum of the all angle in a triangle is 180 degrees.

Therefore we have

The Z+43+52+40=180

Z+125=180

Z=55

Therefore in a triangle degree 52 degrees and 40 degree

y+52+40=180

y+92=180

y=180-92

y=88 degrees

For the angle x, we have

x+15+40+52=180

x+107=180

x=180-107

x=73

The value of the angles x,y, and z is 73 degrees,88 degrees, and 55 degrees.

To learn more about the angle visit:

https://brainly.com/question/25716982

#SPJ1

To solve the equation -2x²-x+1=0 using the quadratic formula, what would be the value of b?
0
-2
-1
1

Answers

Answer: -1

Step-by-step explanation:

The value of b is the coefficient of x.

find the number of primes less than 190 using the principle of inclusion-exclusion.

Answers

The number of primes less than 190 using the principle of inclusion-exclusion are 42

Principle of inclusion- exclusion

The principle of inclusion-exclusion is known as a counting technique that computes the number of elements satisfying at least one of several properties and guaranteeing that the numbers are not counted twice.

Prime numbers are numbers only divisible by 1 and itself.

Prime numbers less than 190 are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181

They are 42 in number

Therefore, the number of primes less than 190 using the principle of inclusion-exclusion are 42

Learn more about prime numbers here:

https://brainly.com/question/874965

#SPJ11

Solve for X
2x+ 17
3x-4

Answers

Answer:

x = 21

Step-by-step explanation:

3x - 4 = 2x + 17 because of alternate angles

3x - 2x = 17 + 4

x = 21

0.738×0.28 is 0.20664 but is rounded to 0.21. which rule or rules are applied to this calculation? select all that apply.

Answers

The rules of the calculation are:

Round the result to the same number of significant figures as the value with the least number of significant figuresRound up if the digit to be dropped is 5 or greater.

How to determine the rule?

The complete question is added as an attachment

The equation is given as:

0.738 × 0.28 = 0.20664

When approximated, we have:

0.738 × 0.28 ≈ 0.21

The above approximation can mean any of the following:

To 2 decimal placesTo the nearest hundredthTo 2 significant digits

Answers

Answer:

18-10-1

Step-by-step explanation:

please mark me as brainlest

Answer:

18-7+3-1

18-10-1

18-11

+7 or 7

Step-by-step explanation:

we have first done of bracket

then as we know minus and minus is equal to plus

then we have done our solution

thank you

What is the inverse of the function g(x)=-3(x + 6)?
Please help me ASAP

Answers

Answer:

Inverse g(x) = -x/3-6

Step-by-step explanation:

To understand this just think g(x) as y so

we got y= -3(x+6) after that we change the minus three to left

so we got -y/3 because -3 is multiply. After that plus 6 came and become minus 6.

After all,you have to replace x in y place.

y = -3(x +6)

-y/3 = x +6

-y/3 -6 = x

-x/3 -6 = g(x)

Find a polynomial function of least degree having only real coefficients, a leading coefficient of 1, and roots of 1-√6 , 1+ √6 , and 7-i

Answers

Step-by-step explanation:

Use this algebra 2 theorem:

If r and q are roots of a polynomial function then

the polynomial function can be expressed as

[tex](x - r)(x - q)[/tex]

Here the roots are

1- root of 6, 1+ root 6, and. 7-i so our. function can be expressed as

[tex](x - (1 - \sqrt{6} ))(x - (1 + \sqrt{6} ))(x - (7 - i))[/tex]

The first two binomials are difference off squares so the we have

[tex] {x}^{2} + x( - 1 + \sqrt{6} ) + x( - 1 - \sqrt{6} ) + ( - 5)[/tex]

[tex] {x}^{2} - 2x - 5[/tex]

The other root is (7-i).

Also note since (7-i) is a root, then (7+I) is also a root.

[tex](x - (7 - i)(x - (7 + i)( {x}^{2} - 2x - 5)[/tex]

[tex]( {x}^{2} - 14x + 50)( {x}^{2} - 2x - 5)[/tex]

Simplify and it gives us

[tex] {x}^{4} - 16 {x}^{3} + 73 {x}^{2} - 30x - 250[/tex]

What type of polynomial is P(X)=1-2x^2+3x+2x^5

Answers

That is a polynomial itself because it is more than a 3 terms. This terms include an operation to be classified as “term”

Determine the measure of each indicated angle.

Answers

The value of x is +2 and -2 and the angles will be given as ∠ABC = 52 ∠ACB = 48 and ∠CAB = 80.

What is trigonometry?

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

Given that:-

∠ABC = 13x² ∠ACB = 12x² and ∠CAB = 20x²

The angles will be calculated as follows:-

13x² + 12x² + 20x² = 180

45x² = 180

x² = 4

x = ±2

The angles will be:-

∠ABC = 13x² = 13 x ( 2² ) = 52

∠ACB = 12x² = 12 ( 2² ) = 48

∠CAB = 20x² = 20 ( 2² ) = 80

Therefore value of x is +2 and -2 the angles will be given as ∠ABC = 52 ∠ACB = 48 and ∠CAB = 80.

To know more about Trigonometry follow

https://brainly. com/question/24349828

#SPJ1

How do I solve an endless amount of numbers with a common ratio
..........

etc. 10+1+0.1+0.01+0.001....

Answers

Answer:

11 .21 add the number together

Notice that the given sum is equivalent to

[tex]10 + 1 + \dfrac1{10} + \dfrac1{10^2} + \dfrac1{10^3} + \cdots \\\\ ~~~~~~~~~~~~ = 10 \left(1 + \dfrac1{10} + \dfrac1{10^2} + \dfrac1{10^3} + \dfrac1{10^4} + \cdots\right)[/tex]

or 10 times the infinite geometric series with ratio 1/10.

To compute the infinite sum, consider the [tex]n[/tex]-th partial sum

[tex]S_n = 1 + \dfrac1{10} + \dfrac1{10^2} + \cdots + \dfrac1{10^{n-1}}[/tex]

Multiply both sides by the ratio.

[tex]\dfrac1{10} S_n = \dfrac1{10} + \dfrac1{10^2} + \dfrac1{10^3} + \cdots + \dfrac1{10^n}[/tex]

Subtract this from [tex]S_n[/tex] to eliminate all but the outermost terms,

[tex]S_n - \dfrac1{10} S_n = 1 - \dfrac1{10^n} \implies S_n = \dfrac{10}9 \left(1 - \dfrac1{10^n}\right)[/tex]

As [tex]n\to\infty[/tex], the exponential term will decay to 0, leaving us with

[tex]1 + \dfrac1{10} + \dfrac1{10^2} + \cdots = \dfrac{10}9[/tex]

Then the value of the sum we want is

[tex]10\times\dfrac{10}9 = \boxed{\dfrac{100}9}[/tex]

The circle graph shows the results of a survey of registered voters the day of an election.
The error given in the graph means that the actual percentage could be 2% more or 2% less than the parent reported by the survey.
What are the minimum and maximum percentages of voters who could vote Republicans? Green?
How can you use absolute value equations to represent your answers in part (a)?
One candidate receives 44% of the vote, Which party does the candidate belong to? Explain.

Answers

The minimum and maximum percentages of voters who could vote Republicans are 40% and 44% respectively, while Green are 0% and 4%

The minimum and maximum percentages of voters in Republicans? Green?

The attached circle graph represents the missing information in the question.

From the graph, we have:

Republicans = 42%

Green = 2%

The actual percentage is given as: ±2%

So, we have:

Republicans = 42% ± 2% = (40%, 44%)

Green = 2% ± 2% = (0%, 4%)

Hence, the minimum and maximum percentages of voters who could vote Republicans are 40% and 44% respectively, while Green are 0% and 4%

The absolute value equations of part (a)?

We have:

The actual percentage is given as: ±2%

Let the number of votes be on the circle graph be x and the range be y.

So, we have:

y - x = ±2%

Express as absolute value equation

|y - x| = 2%

For Republicans, we have:

|y - 42%| = 2%

For Green, we have:

|y - 2%| = 2%

Hence, the absolute value equations are |y - 42%| = 2% and |y - 2%| = 2%

The party of candidate that receives 44% vote

In (a), we have:

Republicans = 42% ± 2% = (40%, 44%)

Hence, the party of candidate that receives 44% vote is Republican

Answers

Answer:

See below

Step-by-step explanation:

This is a line and a parabola......where they intersect the two equations are equal :

2x+7 = x^2 - 1

x^2 - 2x -8 = 0

(x-4)(x+2) = 0 shows the x-coordinate for intersections at x = 4 and -2

sub these x values into one of the equations to calculate the y coordinate

y = 2(4) + 7 = 15 so one point is 4,15

y = 2(-2) + 7 = 3 the other point is then -2, 3

Look at the pattern.

What is the next image in the pattern?

Answers

By following the pattern the next image in the pattern is (b) since the correct option is (b).

A recurring arrangement of numbers, forms, colors, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers is arranged in a particular way, the arrangement is referred to as a pattern.

From the pattern given: In pattern one, the first column contains 2 blocks and the second column contains 1 block. In pattern second, the first column contains 3 blocks, the second column contains 2 blocks and the third column contains 1 block. In pattern third, the first column contains 4 blocks, the second column contains 3 blocks, the third column contains 2 blocks and the fourth column contains 1 block.

∴ You can observe that block the ks are arranged in descending numbers.

Hence, option (b) is correct.

Learn more about patterns here: https://brainly.com/question/534678

#SPJ10

An architect is designing new housing structures for the primate section at the zoo. Her plan is shown below. Which animals will live in a building that is similar to the main primate house? A orangutans B chimpanzees C gibbons D gorillas

Answers

Answer:

Step-by-step explanation:

Reflect shape A in the x-axis.
I have 20 min to complete this

Answers

Answer:

Step-by-step explanation:

Function h is a transformation of the parent exponential function. Which statement is true about this function? h(x)=2^x-5

Answers

A function assigns the values. The correct option is C.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The complete question is:

Function h is a transformation of the parent exponential function. Which statement is true about this function? h(x) = 2^(x-5)

As x approaches negative infinity, h(r) approaches negative infinity.

As x approaches positive infinity, h(t) approaches 0.

As x approaches positive Infinity, h(t) approaches positive infinity.

As x approaches negative infinity, h(a) approaches positive infinity.

The graph of the function is given below, as it can be observed that as x approaches positive Infinity, h(t) approaches positive infinity.

Hence, the correct option is C.

Learn more about Function:

https://brainly.com/question/5245372

#SPJ1

Does the taxable capital gains added to the banker’s income move them to a higher tax rate?

Answers

The taxable capital gains added to the banker’s income move them to a higher tax rate. the statement is true.

What is income tax?

Income tax is a tax applied on individuals or entities concerning income or profit earned by them.

Qualified plans provide two tax benefits that are not available in other types of investments.

Tax rates will be higher in the future with the increment of time, but the benefits of the tax-deferred savings plan will overcome higher tax rates over time.

The taxable capital gains added to the banker’s income move them to a higher tax rate. the statement is true.

Learn more about tax;

https://brainly.com/question/15708726

#SPJ1

I need help!!!!
True OR False
------------------------
m - 63 = 37, m = 100?

Answers

Answer:

The answer is true!!!

Step-by-step explanation:

If m=100, 100-63=37 which is true.

Answer: A) True

Detailed Solution:

m - 63 = 37
m = 63 + 37
=> m = 100

Therefore, m = 100 so this Statement is True.

Find The Distance Between4.5 And -1.4. ( i Need A Answer Right Now Pleaseeeeee!!!!!!

Answers

Answer:

5.9

Step-by-step explanation:

The distance between a point A and a point B is A-B. (4.5) - (-1.4) is the same as 4.5 + 1.4 so your answer is 5.9

Answer:

Step-by-steDistance between

(

−

4.5

−

4.5

)

and

(

3.5

)

√

2p explanation:

Hence distance between

(

−

4.5

−

4.5

)

and

(

3.5

)

is given by

√

(

3.5

−

(

−

4.5

)

(

3.5

−

(

−

4.5

)

√

128

√

please answer this i need helppp

Answers

Answer:

D. between 5.4 cm and 6.5 cm

Step-by-step explanation:

The segment is about 6cm
and 6cm is between 5.4 and 6.5

How to do proportional relationships in math 7th grade ?? Please explain ?!!

Answers

Answer:

Try searching online

Step-by-step explanation:

go to your browser then search up
How to do proportional relationships in math 7th grade ?? Please explain ?!!

Help asap!!! For a brainlest

33+6f<33

Shoe your work and steps

Answers

Answer:

f < 0

Step-by-step explanation:

33 + 6f < 33 ( subtract 33 from both sides )

6f < 0 ( divide both sides by 6 )

f < [tex]\frac{0}{6}[/tex] , that is

f < 0

I need help with this math question (Img included)

Answers

Answer: C. 5
Because (x^(2/3))(x^(3/3))=x^(5/3)

A function is a rule thats assigns each value of the independent variable to exactly ____ value of he dependent variable.

Free response:

Answers

A function assigns the values. A function is a rule that assigns each value of the independent variable to exactly each value of the dependent variable.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The given statement can be completed as given below.

A function is a rule that assigns each value of the independent variable to exactly each value of the dependent variable.

Learn more about Function:

https://brainly.com/question/5245372

#SPJ1

Kyle borrows $25000 at 6% p.a. simple interest for four years. Calculate the monthly repayment required to pay this loan off in 48 equal instalments.

Answers

Answer:

$587.13

Step-by-step explanation:

Monthly Payment Formula

[tex]\sf PMT=\dfrac{Pi(1+i)^n}{(1+i)^n-1}[/tex]

where:

PMT = monthly paymentP = loan amounti = interest rate per month (in decimal form)n = term of the loan (in months)

Given:

P = $25,000i = 0.005n = 48

To calculate i, divide the interest rate per annum by 12 and convert to decimal form:

[tex]\implies \sf i=\dfrac{6\%}{12}=\dfrac{0.06}{12}=0.005[/tex]

Substitute the given values into the formula and solve for PMT:

[tex]\implies \sf PMT=\dfrac{25000 \cdot 0.005(1+0.005)^{48}}{(1+0.005)^{48}-1}[/tex]

[tex]\implies \sf PMT=\dfrac{125(1.005)^{48}}{(1.005)^{48}-1}[/tex]

[tex]\implies \sf PMT=587.1257262...[/tex]

Therefore, the monthly repayment required to pay this loan off in 48 equal installments is $587.13 (nearest cent).

Learn more here:

https://brainly.com/question/27811238

Calculate X+Y it in a row way 9

Answers

69! I calculated it by 69-3

When a range of values is used to estimate a population parameter, it is called a. A point estiamte b. A range estimate c. A statistical parameter d. An interval estimate.

Answers

[tex] \: \huge \underline \mathbb{ \green{Answer}} \\ \\ \: \: \tt \boxed{\blue{d. \: \: an \: \: interval \: \: estimate}}[/tex]

the price of an mp3 player is increased by 8%to £52.92
what was the original price?

Answers

Answer:

49£

Step-by-step explanation:

the price of an mp3 player is increased by 8%to £52.92

what was the original price?

52.92 = 108%

52.92 : 108 = 0.49

0.49 * 100 = 49£

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

check

49 * 1.08 = 52.92

the answer is good

A friend of yours was interested in determining whether the news media noticed campus events. Your friend decided to do a content analysis of the local paper.Your friend counted each story that mentioned his university's name. At the end of two months, 136 events had been counted. Your friend asked for your comments on his research. You told your friend:

Answers

The inference is that the person will tell the friend that he did manifest coding and he should have recorded the base.

What is an inference?

The options are:

He did manifest coding.

He did latent coding.

He should have recorded the base.

He did manifest coding and he should have recorded the base.

It should be noted that an inference simply means the conclusion that can be deduced based on the information given.

In this case, the friend was interested in determining whether the news media noticed campus events and decided to do a content analysis of the local paper.

Therefore, the the person will tell the friend that he did manifest coding and he should have recorded the base.

Learn more about inference on:

brainly.com/question/25280941

#SPJ12

You told your friend: d. he did manifest coding and he should have recorded the base.

How to determine the true statement?

The missing options are:

a. he did manifest coding. b. he did latent coding.

c. he should have recorded the base.

d. he did manifest coding and he should have recorded the base.

e. he did latent coding and he should have recorded the base.

From the question, we understand that:

Each story is counted136 events were counted after 2 months

As a general rule, manifest coding include making use of the contents at the surface gotten from available data and questionnaires.

Because the stories that mentioned the university name can be gotten from publications, it means that your friend used manifest coding

Hence, the true statement is (d) he did manifest coding and he should have recorded the base.