What us the third step in sketching the graph of a rational function

Answers

Answer 1

The third step in sketching the graph of a rational function is "Finding the function's zeros and vertical asymptotes and plotting them on a number line".

What is vertical asymptotes?

A graph's vertical asymptote is a vertical line with the equation x = a, where the graph tends to positive or negative infinity as the inputs get closer to the value of a. A graph's horizontal asymptote is a horizontal line with the equation y = b, where the graph approaches the line as the inputs go closer to ∞ or –∞.

The steps to sketch a graph of rational function:

1. Ensure that the function's denominator and numerator are listed in decreasing order of power.

2. Discover the domain

3. Completely factor the numerator and denominator. Any shared factors between the numerator and denominator should be eliminated. (Once factors have been cancelled, the reduced function is what remains. For all subsequent actions, employ the reduced function.) Skip Step 4 if there are no common factors.

4. Look for any holes

5. Search for any vertical asymptotes.

6. Find the Horizontal Asymptote.

7. Look for any x- and y-intercepts.

8. Locate test points

To learn more about rational function, click on below link:

https://brainly.com/question/13008547

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Related Questions

Is anyone able to help me out with this???

Answers

Answer:

x = 24

Step-by-step explanation:

To simplify the work we can use the Pytaghoran theorem in this way:

x^2 + x^2 = (24√2)^2

2x^2 = 24^2 *(√2)^2

2x^2 = 576 * 2

x^2 = 576

x = +/- √576

x = +/- 24

we choose only the positive value because a length can’t be negative

x = 24

What is 7.37 as a fraction

Answers

Answer:

737/100

Step-by-step explanation:

A pizza parlor sells pizza in two sizes, a 16 inch pizza or a 10inch pizza. Which is more pizza, half of the 16-inch pizza or the entire inch pizza?

Topic: arc length and sector area

Answers

Answer:

Therefore the second pizza of 10inch is More

Y>X

Step-by-step explanation:

From the question we are told that:

Diameter of pizzas

Pizza one [tex]D_1=16[/tex]

Pizza two [tex]D_2=10[/tex]

Generally the equation for amount of half of pizza one X is mathematically given by

[tex]X=\frac{1}{2}\pi r^2[/tex]

[tex]X=\frac{1}{2}\pi 8^2[/tex]

[tex]X=100.53inch^2[/tex]

Generally the equation for amount of pizza two Y is mathematically given by

[tex]Y=\pi r^2[/tex]

[tex]Y=\pi 10^2[/tex]

[tex]Y=314.16inch^2[/tex]

Therefore the second pizza of 10inch is More

Y>X

Answer:

26

Step-by-step explanation:

How many ten thousand are there in 50,000​

Answers

Answer:

5 ten thousands

Step-by-step explanation:

Ten thousands: 10,000

So...

50,000/10,000=5

5 ten thousands

5 since there are 5 digits I hope this helps!

Subtracting fractions with unlike denominators

Answers

your awnser will be 1 3/4

Answer:

[tex]\frac{9}{4} - \frac{5}{10} = 1\frac{3}{4}[/tex]

Step-by-step explanation:

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

LCD(9/4, 5/10) = 20

[tex](\frac{9}{4} * \frac{5}{5} ) - (\frac{5}{10} * \frac{2}{2} ) = ?[/tex]

Complete the multiplication and the equation becomes

[tex]\frac{45}{20} - \frac{10}{20}[/tex]

The two fractions now have like denominators so you can subtract the numerators.

Then:

[tex]\frac{45 - 10}{20} = \frac{35}{20}[/tex]

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 35 and 20 using

GCF(35,20) = 5

[tex]\frac{35 / 5 }{20 / 5} = \frac{7}{4}[/tex]

The fraction

[tex]\frac{7}{4}[/tex]

is the same as

7 ÷ 4

Therefore:

[tex]\frac{9}{4} - \frac{5}{10} = 1\frac{3}{4}[/tex]

Apply the fractions formula for subtraction, to

[tex]\frac{9}{4} - \frac{5}{10}[/tex]

and solve

[tex]\frac{(9 * 10)- (5* 4) }{4 * 10}[/tex]

[tex]= \frac{90-20}{40}[/tex]

[tex]= \frac{70}{40}[/tex]

Reduce by dividing both the numerator and denominator by the Greatest Common Factor GCF(70,40) = 10

[tex]\frac{70/ 10 }{40 / 10} = \frac{7}{4}[/tex]

Convert to a mixed number using

long division for 7 ÷ 4 = 1R3, so

[tex]\frac{7}{4} = 1\frac{3}{4}[/tex]

Therefore:

[tex]\frac{9}{4} - \frac{5}{10} = 1\frac{3}{4}[/tex]

Name the quadrilateral that has a right angle and four congruent sides.
A. Parallelogram
B. Rectangle
C. Rhombus
D. Square

Answers

Answer:

D. Square

It is the only one with all right angles and sides the same length

A farmer sells 8.1 kilograms of apples and pears at the farmer's market. 2 5 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market?

Answers

The question is incomplete:

A farmer sells 8.1 kilograms of apples and pears at the farmer's market. 2/5 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market?

Answer:

She sold 4.86 kg of pears at the farmer's market.

Step-by-step explanation:

With information provided, you know the amount of kilograms of  apples and pears sold and that 2/5 of this weight is apples, so you can find first the number of kilograms of apples sold by multipying 2/5 for 8.1 kilograms:

2/5*8.1=3.24 kg

Now, you can find the kilograms of pears that the farmer sold by subtracting the kilograms of apples sold from the total amount of apples and pears sold:

8.1-3.24=4.86 kg

According to this, the answer is that she sold 4.86 kg of pears at the farmer's market.

Hello, can you help me please​

Answers

Step-by-step explanation:

1. C(x) is in vertex form so let write the function out.

[tex]a(x - 1) {}^{2} + b[/tex]

B is our maximum value so b=9.

[tex]a(x - 1) { }^{2} + 9[/tex]

To find a, we know that when x=5 is a root so plug 5 in for x to find a.

[tex]a(5 - 1) {}^{2} + 9 = 0[/tex]

[tex]a(4) {}^{2} + 9 = 0[/tex]

[tex]16a = - 9[/tex]

[tex]a = - \frac{9}{16} [/tex]

2.. Let convert Chelesa function into. standard form.

[tex] \frac{ -9 }{16} (x - 1) {}^{2} + 9[/tex]

[tex] - \frac{9}{16} (x {}^{2} - 2x + 1) + 9[/tex]

[tex] - \frac{9}{16} {x}^{2} + \frac{9}{8} x + \frac{135}{16} [/tex]

Let see which value has the higher constant.

135/16 is more than 8 so Chelsea jumper higher.

3. Set Herritea equation equal to zero.

[tex] - \frac{2}{9} {x }^{2} + 8 = 0[/tex]

[tex] - \frac{2}{9} x {}^{2} = - 8[/tex]

Multiply both sides by the reciprocal of negative 2/9.

[tex] {x}^{2} = - 8 \times - \frac{9}{2} [/tex]

[tex] {x}^{2} = 36[/tex]

[tex]x = 6[/tex]

We talking positive distance so the answer is she has moved 6 units horinzontial.

4. The domain of C is all real numbers and the range is All real numbers that are less than or equal to 9.

The domain of H is all real numbers, the range of H is all real numbers that are less than or equal to 8.

5. That means that the y values are equal when x=3.7

21 = -3c + 7 -5c -2

i need help with this multi step equation question​

Answers

Answer:

c=-2

Step-by-step explanation:

I need an answer ASAP!!

Answers

Answer:

CD=13

Step-by-step explanation:

The figure is symmetrical, as evidenced by the angle measures being marked at the top.

Answer:

13

Step-by-step explanation:

If you look up at the top, you can see that there is two angles that are the same, so that must mean that it can be folded down perfectly.

hope this helps!

The question is in the photo.

Answers

Answer and Step-by-step explanation:

[tex]\frac{9}{10}[/tex] ÷ [tex]\frac{4}{10}[/tex]

([tex]\frac{2}{5}[/tex] × [tex]\frac{2}{2} = \frac{4}{10}[/tex])

[tex]\frac{9}{10}[/tex] ÷ [tex]\frac{4}{10}[/tex] = [tex]\frac{90}{40} = \frac{9}{4} = 2.25[/tex] - This is the answer.

#teamtrees #PAW (Plant And Water)

Find the 53rd term of the arithmetic sequence -12, -1, 10

Answers

440 is the answer

Tn=a+(n-1)d

Tn=53

a= -12

n=53

d= 11

-12+(53-1)11 = 440

Answer:

560

Step-by-step explanation:

The sequence above is an arithmetic sequence

For an nth term in an arithmetic sequence

A(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

Since we're finding the 53rd term

a = - 12

n = 53

d = -1 - ( -12) = - 1 + 12 = 11 or 10--1 = 10 +1 =11

d = 11

So we have

A(53) = - 12 + (11)(53 - 1)

= - 12 + 11(52)

= -12 + 572

= 560

We have the final answer as

560

Hope this helps you

A triangular prism has a triangular face with a base of 8.8 meters and a height of 10.7 meters. Its volume is 941.6 cubic meters. What is the length of the triangular prism?

Answers

Answer:

yo wanna know want to know wants I had that problem you do...

The answer is 10 ez

Step-by-step explanation:

10.7*8.8 which is 94.16

and then you divide that by 941.6/94.16=10 so then answer is 10

Martha ordered 3 cheesecakes. She will cut each cake into fourths. How many pieces of cake will she have?

Answers

12 because there are 3 cakes and cutting each into 4..... 3x4=12

In PQR the measure of R=90, QR=61 feet and RP=90 find the measure of P to the nearest degree.

Answers

Answer:

<P = 56 degrees

Step-by-step explanation:

Given the following

m<R = 90 degrees

QR = 61feet = Adjacent

RP = 90 feet= Opposite

Required

tan<P = opp/adj

Tan<P = 90/61

<P = arc tan (90/61)

<P = arctan 1.4754

<P = 55.9

<P = 56 degrees to the nearest degree

A circle is inscribed in a square with a side length of 144. If a point in the square is chosen at random, what is the probability that the point is inside the circle?

Answers

Given :

A circle is inscribed in a square with a side length of 144.

So, radius of circle, r = 144/2 = 72 units.

To Find :

The probability that the point is inside the circle.

Solution :

Area of circle,

[tex]A_c = \pi r^2\\\\A_c = 3.14 \times 72^2\ units^2\\\\A_c = 16277.76 \ units^2[/tex]

Area of square,

[tex]A_s = (2r)^2\\\\A_s = ( 2 \times 72)^2\ units^2\\\\A_s = 20736\ units^2[/tex]

Now, probability is given by :

[tex]P = \dfrac{A_c}{A_s}\\\\P = \dfrac{16277.76}{20736}\\\\P = 0.785[/tex]

Therefore, the probability that the point is inside the circle is 0.785 .

9. The gradient of the curve y=kx⁴ at the point x = 2 is 128. Find the value of k.​

Answers

Answer:

k = 4

Step-by-step explanation:

Here, we want to find the value of k

Mathematically, the gradient of a curve is same as the first derivative

so the first derivative here is;

dy/dx = 4kx^3

Now, the value of x here is 2 while the value of y is 128

Substituting these values;

128 = 4k(2)^3

128 = 32k

k = 128/32

k = 4

Factor completely:
3x2 - 75

Answers

Answer:

3(x + 5)(x − 5)

Step-by-step explanation:

Since both terms are perfect squares, factor using the difference of squares formula:

a² − b² = (a + b)

(a − b)  

where  a = x and  b = 5.

3(x + 5)(x − 5)

Or

Search it up for a more detailed answer through Goo gle.


One angle of a right triangle measures 8º. What is the measure of the other acute angle?

Answers

82 degrees. Cause 180- (8+90)

Someone help please !!

Answers

Answer:

what grade is this?

What is the selling price per widget as a function of the
number of widgets produced, and what should the
selling price be if 15 widgets are produced?

Answers

Answer:

1240 widgets

Step-by-step explanation:

The value of the function at 870, the local maximum, is

= -0.02(870)2 + 34.80(870) - 4700

= -0.02(756900) + 30276 - 4700

=  -15138 + 25576

= 10438

 

So the vertex is (870, 10438)

 

The cost t the company to produce 870 widgets is  

C(870) = 4700 + 5.20(870) = 4700 + 4524 = 9224

 

So, the cost of the widgets plus the profit must be equal to the total sales, which is divided by the number of widgets reveal their individual price.

(10438 + 9224)/870 = 19662/870 = $22.60

 

P(x) = 7700

- 0.02x2 + 34.80x - 4700 = 7700

-0.02x2 + 34.80x -12400 = 0

 

x = {-34.80 ± √[(34.80)2 - 4(-0.02)(-12400)]}/2(-0.02)

x = [-34.80 ± √(1211.04 - 992)]/(-0.04)

x = (-34.80 ± √219.04)/(-0.04)

x = (-34.80 ± 14.8)/(-0.04)

x = 870 ± 370

so, $7700 in profits will be earned at either 500 widgets or 1240 widgets

44% of what number is 11?

Answers

25

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HELP PLSSSSSSSSSSSSS

Answers

Answer:

x=9

Step-by-step explanation:

Since, these angles are identified as vertical angles, both sides are equal to each other. So, in order to solve this problem, we have to set the equations equal to each other: (7x+3 = 10x-24).

please help me please will give brainliest ​

Answers

Answer:

it's the 3rd option (eeeexxxxttteeennndddeeerrr)

Answer:

the correct answer is c i hoped this helped

Find the measure of the indicated arc

Answers

Answer:

m(arc WXY) = 224°

Step-by-step explanation:

By inscribed angle theorem,,

"Measure of intercepted arc is double of the inscribed angle"

m(arc WXY) = 2[m(∠YCW)]

Here, arc WXY is the intercepted arc and ∠YCW is the inscribed angle.

By substituting the value of inscribed angle,

m(arc WXY) = 2(112°)

                     = 224°

Therefore, measure of arc WXY is 224°.

The vertex of this parabola is at (-2, 1). Which of the following could be its
equation?
(-2.1)
5
O A. x = 4(y + 1)2. 2
O B. y = 4(x - 2)2 +1
O C. x = 4(y - 1)2 - 2
O D. y = 4(x - 2)2 - 1

Answers

Answer:

y = 4(x + 2)^2 + 1   (Answer B)

Step-by-step explanation:

Here we're given h = -2 and k = 1.  Right away we know that the vertex form of the pertinent equation is

y = 4(x + 2)^2 + 1   (Answer B)

6) Determine the dimensions of a rectangle if:

A = x2 – 19x – 90

Answers

Answer:

Step-by-step explanation:

Determine the dimensions of a rectangle if:

A = x2 – 19x – 90

Can someone please help me with math.

Answers

9 is c. 10 is d. And 11 is c.

Using 3.14 for n, what is the volume, to the nearest tenth, of a cone that has a height and of 16 feet and a base with radius 5 feet

Answers

Answer: 418.7

Step-by-step explanation:

https://www.calculatorsoup.com/calculators/geometry-solids/cone.php

2x + 46 + 3x - 6
I forgot how to do math

Answers

Answer: hope this helps

Step-by-step explanation:

5 (x + 8)

Root:

x = -8

Derivative:

d/dx(2 x + 46 + 3 x - 6) = 5

Indefinite integral:

integral(40 + 5 x) dx = (5 x^2)/2 + 40 x + constant

Answer:

5x-40=0

5x=40

x=40/5

x=8

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