f(x)= x^2 - 4x / x^2 - x - 2

find the x and y intercepts

find vertical and horizontal asymptotes

determine the holes

Answers

Answer 1

Step-by-step explanation:

First, I decided to determine the vertical asymptote! You can determine the vertical asymptote by taking the denominator and setting it equal to zero.

−4x+4=0

−4x=−4

x=1

There's a vertical asymptote at x=1.

Now for the horizontal asymptote! The horizontal asymptote is determined by looking at the leading coefficients in the numerator and denominator. Here's a helpful visual.

content://com.cryptotab.android.FileProvider/images/screenshot/16159519510813476709092178134526.jp

In our case, the leading coefficient in the numerator (x2) is larger than the leading coefficient in the denominator (−4x). This means there is no horizontal asymptote!

In some cases, a slant asymptote may be present in a graph. These are sometimes present in graphs that have a stronger leading coefficient in the numerator than the denominator. To determine the slant asymptote, we need to divide the numerator by the denominator.

content://com.cryptotab.android.FileProvider/images/screenshot/16159520052041557972364765603410

The slant asymptote is y=−x4−1

Holes are determined by finding numbers that when plugged into x, return undefined. On a graphing calculator these values will give us an error. Luckily for us, there are no holes, so we can move on.

X-intercepts are values that make the numerator equal zero. We can find these by setting the numerator equal to zero and solving.

x2+3x=0

x(x+3)=0

x+3=0

x=−3

Another number that makes the numerator equal zero is, well, zero!

x2+3x=0

(0)2+3(0)=0

0=0

So we know our x-intercepts are 0 and -3.

To find the y-intercepts, set x equal to zero and solve the equation!

y=x2+3x−4x+4

y=(0)2+3(0)−4(0)+4

y=04

y=0

So we have a y-intercept at y=0!


Related Questions

what is y= -3x + 4 what does y equal

Answers

Please don’t try searching up that link the same person did the same to me on my question

y = 3x-4

Serge was curious if a sample third quartile was an unbiased estimator of a population third quartile. He started with a large normally distributed population of test scores whose third quartile was Q3=80 points. He then took a random sample of 6 tests and calculated the third quartile of the sample. He replaced those tests and repeated this process for a total of 40 trials. His results are summarized in the dot plot below, where each dot represents the third quartile from a sample of 6 tests.

Answers

Answer:

Sample third quartile appears to be an unbiased estimator of the population third quartile.

Step-by-step explanation:

khan

Find the quotient
6 1/2 divided by 3/4

Answers

Answer:

8 2/3

Step-by-step explanation:

First, we turn 6 1/2 into an improper fraction, which is 13/2. Now, we can write this out as: 13/2  divided by 3/4. When dividing fractions, you reverse the sign to multiplication and you flip the numerator and the denominator of the second number. So, in this case, it would be 13/2 TIMES 4/3 which now we can do! 13*4 is 52 and 2*3 is 6. 52/6 is a number we can simplify. We can divide out a 2, so 52/2 is 26 and 6/2 is 3. 26/3 can be put into a mixed number. 3 goes into 26, 8 times and there is a 2 left over. So our final answer is 6 2/3.

#13: The difference between two numbers is 3. Their sum if 27. What is the smaller number? * Your answer​

Answers

Answer:

The smaller number is 12 & greater number is 15.

Answer:

12

Step-by-step explanation:

let the numbers be x and y and x>y

x-y=3

x+y=27

add

2x=30

x=30/2=15

15+y=27

y=27-15=12

When the angle of elevation of the sun is 50 degrees, a flagpole casts a shadow that is 16.8 feet long. What is the height of the flagpole to the nearest foot?

Answers

The answer is 50 degrees angle

what's 100,994 rounded to the nearest 100?

Answers

Answer: 101000

Step-by-step explanation: It would be rounded to 101000 because the nearest 100 would be a 1000.

Answer: 111,000 because when you round 994 you get a thousand because that’s the next hundred so you get 111,000

Step-by-step explanation:

Which of the following number lines represents the inequality below?

Answers

Answer:

B

Step-by-step explanation:

The circle has to be hallow in order for it to be greater than or less than. The arrow is going below 4 because the circle is on 4 and the arrow is pointing to the left side.

Answer:

B

Step-by-step explanation:

it shows all the numbers less than four while the others show numbers greater than 4

Evaluate the expression:
(-1/7)^0

Please show work


A) -1/7

B) 0

C) 1/7

D) -1

E) 1

F) None of These

Answers

Answer:

The answer is E) 1

Step-by-step explanation:

can you make me brainliest please

PLEASE HELP ASAP!!
Solve for x.

Answers

x=4 and that it's the answer

Identifying When to Use a Sample
ch survey is a sample not necessary?

Answers

The answer is d how many car accidents invoke air bag

what is the value of x in the equation 24 equals 12 - 4x​

Answers

Answer:

x = -3

Step-by-step explanation:

24 = 12 - 4x

24 - 12 = -4x

12 = -4x

12/-4 = x

x = -3

Answer:

x=-3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

24=12−4x

24=12+−4x

24=−4x+12

Step 2: Flip the equation.

−4x+12=24

Step 3: Subtract 12 from both sides.

−4x+12−12=24−12

−4x=12

Step 4: Divide both sides by -4.

−4x

−4

=

12

−4

x=−3

Algebra 2!! What is the domain of the function graphed below?

Answers

Answer:

(-infinity,+infinity)

Step-by-step explanation:

Domain refers to the x-axis. So if we look from left to right along the x-axis we could conclude that the function will go infinitley from negative infinite to positive infinity.

If electricity comes from electrons, does morality come from morons?

Answers

Answer:

AHAHAHAHA

Step-by-step explanation:

nope LOL

Answer:

gftrtrtgfrtrftgtrgty

Step-by-step explanation:

fgrtfgtrfggtrfgtrfgtrfgtrfgytrfgtrfgtr

7.
Find the slope of the line.


A. [tex]\frac{1}{4}[/tex]

B. –4

C. 4

D. [tex]-\frac{1}{4}[/tex]

Answers

Answer:    The answer is either letter A or letter C

home / math / slope calculator

Slope Calculator

By definition, the slope or gradient of a line describes its steepness, incline, or grade.

Where

m — slope

θ — angle of incline

If the 2 Points are Known

Result

Slope (m) =  

ΔY

ΔX

=  

-1

5

= -0.2

θ =  

arctan( ΔY ) + 360°

ΔX

= 348.69006752598°

ΔX = 5 – -5 = 10

ΔY = -3 – -1 = -2

Distance (d) = √ΔX2 + ΔY2 = √104 = 10.198039027186

Equation of the line:

y = -0.2x – 2

or

y =  

- 1 x

5

– -2

When x=0, y = -2

When y=0, x = -10

...............................................................................................................................................

home / math / slope calculator

Slope Calculator

By definition, the slope or gradient of a line describes its steepness, incline, or grade.

Where

m — slope

θ — angle of incline

If the 2 Points are Known

Result

Slope (m) =  

ΔY

ΔX

=  

5

-1

= -5

θ =  

arctan( ΔY ) + 180°

ΔX

= 101.30993247402°

ΔX = -3 – -1 = -2

ΔY = 5 – -5 = 10

Distance (d) = √ΔX2 + ΔY2 = √104 = 10.198039027186

Equation of the line:

y = -5x – 10

When x=0, y = -10

When y=0, x = -2

...............................................................................................................................................

Input Data :

Point A  

(

x

A

,

y

A

)

= (3, 2)

Point B  

(

x

B

,

y

B

)

= (7, 10)

Objective :

Find the slope of a line that passes through points A and B.

Formula :

Slope

 

m

=

y

B

y

A

x

B

x

A

Solution:

Slope

 

m

=

10

2

7

3

=

8

4

m = 2

...............................................................................................................................................

Input Data :

Point A  

(

x

A

,

y

A

)

= (3, 2)

Point B  

(

x

B

,

y

B

)

= (7, 10)

Objective :

Find the slope of a line that passes through points A and B.

Formula :

Slope

 

m

=

y

B

y

A

x

B

x

A

Solution:

Slope

 

m

=

10

2

7

3

=

8

4

m = 2

Step-by-step explanation:    This is the picture, I graphed it

Center: (0, 0)

Angle: 0 rad

Opacity: 1

Width: 10

Height: 6.8


Slove the system
Of Linear Eqitions by
Elimination
3x-y=0
2x+y=-10

Answers

Answer:

(-2, -6)

Step-by-step explanation:

Given the simultaneous equation

3x-y=0 ... 1

2x+y=-10 ... 2

Add both equations to eliminate y

3x + 2x = 0 - 10

5x = -10

x = -10/5

x = -2

Substitute x = -2 into 1

3(-2)- y = 0

-6 - y = 0

-y = 0+ 6

-y = 6

y = -6

Hence the coordinate (x, y) is (-2, -6)

PLEASE HELP!!! ASAP ITS DUE IN 30 MINUTES

Answers

Answer:

.

Step-by-step explanation:

Answer: (4,1)

Step-by-step explanation: Hope this helps :)

Which of the functions (Function A, Function B, or Function C) is quadratic?

Answers

B is quadratic. Im pretty sure it is

If f(a)=4a-5 what is f(3)-f(1.25)
a. -8
b. 7
c. 17
d. 32

Answers

c)17

Step-by-step explanation:

This is for my final grade before spring break please help me asap noww

Answers

Answer:

Bushes are $9.

Bonsai trees are $32.

Step-by-step explanation:

Bushes are b and bonsai trees are t.

15b + 8t = $391

9b + 5t = $241

15b + 8t = $391 × 3 and 9b + 5t = $241 × 5

= 45b + 24t = $1173 and 45b + 25t = $1205

(45b + 24t = $1173) - (45b + 25t = $1205)

t = 1205 - 1173

t = $32

Apply to 15b + 8t = $391.

15b + 32 × 8 = $391

15b = $391 = 32 × 8

15b = $391 - 256

15b = $135

x = ($135 ÷ 15) = $9

A recipe uses 5 cups of milk to make 30 servings. If the same amount of milk is used for each serving, how many servings can be made from one quart?

Answers

Answer:

Three gallons will be enough to make 128 servings.

Step-by-step explanation:

In Three gallons there are 64 cups. if 5 cups makes 10 servings, that is 1/2 cup per serving. So 64 cups will make 128 servings.

Andy is buying a car he negotaited a 7% descrease on £6500 car. he will pay the full balance in 12 equal monthly payments.

Answers

Answer:

he would pay 503.75 every month

Step-by-step explanation:

Drag graphs to show a graph of each equation in the table.

Answers

Answer:

Step-by-step explanation:

- The # in front of x will be the number that hits on the y-axis

- The # after x or the slope, ex: y = -1/2x + 2, is how much you move to hit the next point on the graph

-  2 would actually be 2/1 so move up 2 and right 1 (if the number or fraction is negative then go up and to the left

- So y = -2x - 1/2, negative slope. Start at -2 on y-axis and go up 1 then left 2.

una escalera esta recargada en un muro de 8 metros de altura y forma un angulo agudo de 55 grados ¿cual es la longitud de la escalera?

Answers

Answer:

9.77 metros

Step-by-step explanation:

Ay que usar sine, mira el problema en la photo

Paige mows 1/4 acres in a 1/2 hour. How many acres does page mow per hour?

Answers

Page mows 0.5 acres per hour.

Answer:

2/3 acres per hour.

If y + 10 = 25, what is the value of 3(y + 2)?

Answers

Answer:

3(15 + 2) = 3 x 17 = 51    

Step-by-step explanation:

Answer:

51

Step-by-step explanation:

y=15

3(15+2)

45+6

51


A sector of a circle has an area of 263.42cm and the area of the entire circle has an area of 563.24cm? What is the central angle of the
sector described?

Answers

Answer:

168

Step-by-step explanation:

168 is  the ans is 100% correct

(hope this helps can i plz have brainlist :D hehe)

Brainly for questions 4 & 5

Answers

Answer:

its a quiz you might get banned

Step-by-step explanation:

Which graph below is connected?

Answers

Answer:

number 1 i already answered that and Im correct

Simply expression 7(x+y)-7x

Answers

Answer:

7y

Step-by-step explanation:

7(x + y) - 7x =

= 7x + 7y - 7x

= 7y

Answer:

7y

Step-by-step explanation:

7(x+y)-7x=7x+7y-7x=7y

Hope this helps :)

On circle O below, the measure of SV is 120°.


What is the measure of VU?

Answers

Answer: Angle VU is 44 degrees

Step-by-step explanation:

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