PLEASE HELP ME!!! I WILL MARK THE BRAINLIEST!! A given rational function has a quadratic numerator and a linear denominator. When the function is simplified, the denominator cancels out. The graph will look like:
a- a straight line with a hole
b- two branches with a vertical asymptote and a horizontal asymptote
c- two branches with a vertical asymptote, a horizontal asymptote and a hole
d- a straight line with no hole

Answers

Answer 1

Answer:

D A strait line with a hole because when you cancel you will leave a hole

Step-by-step explanation:

Answer 2

b

Graph the following:

y = (x^2 - x - 2) / (x - 2)

First I'll find any vertical asymptotes, by setting the denominator equal to zero and solving:

x – 2 = 0

x = 2

So I have a vertical asymptote

at x = 2.

I'll dash this in:

graph showing vertical asymptote

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Looking at the degrees of the numerator and denominator, I see that the numerator is a quadratic while the denominator is linear. Since the degree is one greater in the numerator, I know that I will have a slant asymptote. But I need to do the long division to find out what the equation of the slant asymptote is going to be.

long division: (x^2 - x - 2) ÷ (x - 2) = x + 1

Hmm... The slant asymptote is clearly y = x + 1, but there is no remainder; the division came out evenly. That's because the numerator happens to factor as (x – 2)(x + 1), so the x – 2 factor divides out evenly and there is no remainder.

In any case, the slant (not horizontal) asymptote is at y = x + 1:

graph showing slant asymptote

Now I'll find the intercepts: Copyright © Elizabeth Stapel 2003-2011 All Rights Reserved

x = 0: y = (0 – 0 – 2)/(0 – 2) = 1

y = 0: 0 = (x2 – x – 2) / (x – 2)

0 = x2 – x – 2

0 = (x – 2)(x + 1)

x = 2, x = –1

I know that I can't have x = 2, as an x-intercept, because this is actually the vertical asymptote. So I'll ignore that "solution" of the above equation.

The intercepts then are

(0, 1) and (–1, 0):

graph showing intercepts

Now I'll plot a few more points. However, since this example is actually a special case of slant-asymptote problem (and something of a trick question), I'll also show you the points for the slant asymptote only.

x y = (x2 – x – 2)/(x – 2) y = x + 1

–6 y = (36 + 6 – 2)/(–6 – 2) = –5 y = –5

–5 y = (25 + 5 – 2)/(–5 – 2) = –4 y = –4

–4 y = (16 + 4 – 2)/(–4 – 2) = –3 y = –3

–3 y = (9 + 3 – 2)/(–3 – 2) = –2 y = –2

–2 y = (4 + 2 – 2)/(–2 – 2) = –1 y = –1

–1 y = (1 + 1 – 2)/(–1 – 2) = 0 y = 0

0 y = (0 – 0 – 2)/(0 – 2) = 1 y = 1

1 y = (1 – 1 – 2)/(1 – 2) = 2 y = 2

2 — y is not defined — y = 3

3 y = (9 – 3 – 2)/(3 – 2) = 4 y = 4

4 y = (16 – 4 – 2)/(4 – 2) = 5 y = 5

Do you see how that, except for the one point where the rational function isn't defined (at x = 2), the two lines are the same? In general, this is not true for rationals. But in this special case — where the long division works out with no remainder — you don't actually even need the asyptote lines dashed in. Instead, you find the slant asymptote equation (in this case, y = x + 1), and you draw that in for the rational graph.

The only difference between the slant asymptote of the rational function and the rational function itself is that the rational function isn't defined at x = 2. To account for this, I leave a nice big open circle at the point where x = 2, showing that I know that this point is not actually included on the graph, because of the zero in the denominator of the rational.

graph of y = (x^2 - x - 2) / (x - 2)

Warning: This graph is not the norm for rationals. But you should expect to encounter one like this, perhaps on the test. I've only ever seen this done with slant asymptotes, but it could be done with horizontal asymptotes, too. Keep in mind that you can't just "cancel off" duplicate factors when graphing rationals; you still need to account for all the zeroes of the denominator.

Note that your calculator will probably not show this hole in the graph, and "TRACE" will probably miss it too, since it is unlikely that x = 2 will be exactly on the pixel that the calculator is processing. But even if the graph does not show the gap in the line, the calculator will show no value for y when x is two.

When I asked my calculator to evaluate y for x = 2, I got this:

screen shot showing apparently connected line

If it just so happens that the vertical asymptote falls on a pixel (rather than between two pixels), then the gap in the graph will display on the calculator's pretty picture.

For instance, when I changed the window settings on my graphing calculator so the x-values ran from –7 to 7 (rather than the default –10 to 10), the gap was (just barely) visible:

screen shot showing gap in graph

When you do these graphs, get in the habit of working methodically through all the steps (vertical asymptote(s), horizontal or slant asymptote, intercept(s), plotted points, and graph), so you can do the graphing easily when you get to the test. And, as you can see above, you will need to know this material well enough that your calculator doesn't mess you up.


Related Questions

3) 5m - 40
what's da answer ?

Answers

I believe the answer is -8

Solving this you would divide 5m by 5m which cancels 5m out. Then you would divide - 40 by 5m and get -8. Note that you are not actually dividing - 40 by 5m just 5.

Hope this helps!

If Alexander has not sold all of the granola after 3 days, he sells the remaining bags for
60% of the cost. What is the sale price of the individual bags of granola?

Answers

Answer:

Cost Price of Each Bag is 2.5

Total Gain is 17.5

Step-by-step explanation:

Guys please help it’s urgent!! I tried, my friend tried, my mom tried, my brother tried, and no one can get the answer she wants

Answers

Answer:

#13050

Step-by-step explanation:

lxw

30x35= 1050

Answer:

and now i tried

Step-by-step explanation:

hello new challenger (:<

How many degrees is 1.2 rotations counter clockwise?

Answers

Answer:

The expression is already in decimal form.

1.2

Step-by-step explanation:

(づ ̄ ³ ̄)づ

Find exact volume of the cylinder with a diameter of 10 feet and a height of 8 feet

Answers

the exact volume would be 80 feet long

1/3r + 1/6 = 5 5/6

solve this?​

Answers

Answer:

r=17

Step-by-step explanation:

Answer:

r=17

Step-by-step explanation:

1/3r+1/6= 35/6 (5 5/6)

35/6-1/6= 34/6 (5 4/6 or 5 and 2/3)

1/3r= 34/6 (5 4/6)

3*(1/3)r= (34/6)*3

r=17

what is 10% of 50 ??

Answers

Answer:

5

Step-by-step explanation:

10% = 0.1

0.1*50 = 5

Answer:

5

Step-by-step explanation:

10 percent *50 =

( 10:100)*50 =

( 10*50):100 =

500:100 = 5

Now we have: 10 percent of 50 = 5

The figures are similar. Find each missing measure. (Number 6)

Answers

It’s 9
Cuz the shape on the right is 3/4 of the one to the left

6+5 x 2 +5+ =

67 +84 - 12 x 4 = 16

Answers

Answer:

6+(5 x 2)+5=21

the way you wrote this was kinda weird so I don't know what you expected as an answer

Step-by-step explanation:

5 x 2=10

10+6=16

16+5=21

21

If 8x−5y=−3 is a true equation, what would be the value of 8x−5y+7?

Answers

Answer:

Value of 8x -5y + 7 is 4.

Step-by-step explanation:

Given that:

8x-5y = -3     Eqn 1

It is a true equation.

Now we have to find the value of the given expression

8x -5y + 7

Putting value of 8x-5y from Eqn 1 in the given expression

8x - 5y + 7

-3 + 7

4

Therefore,

8x - 5y + 7 = 4

Hence,

Value of 8x -5y + 7 is 4.

The scatter plot shows the maximum noise level when different numbers of the people are in the stadium. The linear model is given by the equation y=1.5x+22.7, where y represents maximum noise level and x represents the number of people the number of people ,in thousands, in the stadium. y=1.5x+22.7

3. What is the y intercept of the linear model given? What does it mean in the context of the problem? Is this reasonable? Explain the reasoning? ​

Answers

The y intercept is 1.5x+22.7 + the linear equation which is 22

The y-intercept of the equation is 22.7 and it represents the initial value of the noise at the y-axis.

What is a scatter plot?

A scatter plot is a type of plot or mathematical diagram that displays values for two variables for a set of data using Cartesian coordinates. One more variable can be displayed if the points are coded.

Given that the scatter plot shows the maximum noise level when different numbers of people are in the stadium. The linear model is given by the equation y=1.5x+22.7, where y represents the maximum noise level and x represents the number of people,in thousands, in the stadium. y=1.5x+22.7

The equation for the maximum noise is given as, y=1.5x+22.7. In the given equation the slope of the line is equal to 1.5. The y-intercept of the equation is 22.7 which represents the initial value of the noise at the y-axis.

To know more about scatter plots follow

https://brainly.com/question/6592115

#SPJ5

In a large-sized fish tank, 65% of the fish are guppies. Which calculation finds the probability of getting less than 60%
guppies in a random sample of 100 fish?
Oplec
0.60 -0.65
.60.00
O Plzc
0.60 -0.65
0.65 (0.35)
100
o plec
0.65 -0.60
0.65(0.35)
100
<
0.50 -0.65
100(0.65)(0.35)
o pſz< 710010.65)(0.35)

Answers

Answer: b

Step-by-step explanation:

find the HCF of the following numbers by prime factorization method 324 & 432​

Answers

Answer:

108

Step-by-step explanation:

324 = 2 * 2 * 3 * 3 * 3 * 3

432 = 2 * 2 * 2 * 2 * 3 * 3 * 3

The HCF is 2 * 2 * 3 * 3 * 3 = 108

Question 2/5
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> NEXT
BOOKMARK
CHECK ANSWER
o
2
Find the area of the triangle below. The area of the triangle is
in
17 in
8in.
10 in.
15 in
6 in

Answers

i think the answer is 122,400

Someone plz help me

Answers

Answer:

16 is the answer hope i helped!

Step-by-step explanation:

Answer:

i think it c

:D

Step-by-step explanation:

Where are all the math whizzes? I need your help, please! I will mark brainliest!
For all positive integers x, y, and z, which of the following expressions equal x/z?

Answers

Answer:

E

Step-by-step explanation:

A. x/yx * zy/yx = 2/x

B. x/y + y/z = (xz+y^2)/yz

C. x*z/z*x = 1

D. (x+y)/(y+z) = y(x+1)/y(1+z) = x+1/1+z

E. x/y / z/y = x/y * y/z = x/z

The graph below represents the linear equation y=1/2x-3 a second linear equation is represented by the data in the table. What is the solution to the system of e

Answers

ik its late but the correct answer is C:(2,-2)

Step-by-step explanation:

I got the answer correct on Edge 2020.

Hope this helps!!

Help me please please

Answers

Answer:

4. c = 10

5. True

6. t = 3

Answer:

#4. 10

#5. true

#6. 3

please help !!!! no wrong answers please please

Answers

Answer:

function

not a function

not a function

function

Step-by-step explanation:

What is the slope of the line that passes through the points (0,7) and (-4,3)

Answers

Answer:

The slope=1

Step-by-step explanation:

(0,7)=(x,y) and (-4,3)=(`x,`y)

The formula for finding slope= `y - y/`x - x

3-7/-4-0

-4/-4

1

Therefore, the slope=1

Help I nee this ASAP, What is the price of 1 tennis ball if a package of three tennis balls cost $4.95?

Answers

Answer:

$1.65

Step-by-step explanation:

4.95/3=1.65

Answer:

One tennis ball costs $1.65

Step-by-step explanation:

?= price of one tennis ball

1   -   ?

3   -   4.95

Solve: 4.95×1÷3= 1.65

Find the value of F, correct to two decimal places

Answers

Answer:

F = 12.14 m

Step-by-step explanation:

F is the side opposite the given 36° angle and the given side length, 15m is adjacent. It's a cosine equation that's needed.

find the cosine of 36°

(calculator necessary)

cos(36) = 0.8090169944

We should be safe to round that to .809 for this.

cos = opp/adj

Substitute what we know:

.809 = F/15 Multiply both sides by 15

.809(15) = F

12.135 = F Round to two places.

Side F is 12.14m

Please I need help this is already late

Answers

the first would be A and hopes this helps

Which best describes the triangle or triangles, if any, that can be formed with the side lengths (not the angles) measuring 60 centimeters, 100 hundred centimeters, and 40 centimeters.

A infinitely many similar scalene triangles
B one unique scalene triangle
C no triangle
D two unique scalene triangles

Will mark brainliest!!!

Answers

Don't be mad if I'm wrong but I think B

Can somebody help me pls

Answers

Answer:

A. don't move either direction

Step-by-step explanation:

the number determines how many you move forward or backward 0 would mean u don't move at all

Answer:

a card with the number 0 would mean not to move at all south would be ''do not move in either direction''

simplify each expression 6X + 2x​

Answers

Answer:

I think the answer is 8x

Answer:

Step-by-step explanation:

6x+2x=(6+2)x

         =8x

What number solves the equation 5(x+12)=95?

Enter your answer in the box.

plz i need an answer asap!

Answers

Answer:

Step-by-step explanation:

5(x+12)=95 (multiply 5 in the brackets)

5x+60=95 (subtract 60 on both sides)

5x=35 (divide 5)

x=7

Solve the simultaneous equations
y = 4x + 1
y = 2x2 + 7x - 1

Answers

Hope that hepled have a nice day

4) Graph the line 2x - 7y = 14 using X- and y-intercepts.
x-intercept y-intercept
Click to add text Click to add text
O
YA
6
5
4
3
2
1
-6-5-4-3-2
1 2 3 4
5 6
2
-3
-5
-6
10:45

Answers

Answer:

(0,-2)   (7,0)

Step-by-step explanation:

Please help me!!!!!””

Answers

Answer:

d=45t

Step-by-step explanation:

to find speed you divide the distance by the time. 67.5/1 1/2 = 45

Answer:d=45t

Step-by-step explanation:

I took the i-Ready

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