1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kirill [66]
2 years ago
8

Part 3 - Discussion/Explanation Question

Mathematics
1 answer:
SpyIntel [72]2 years ago
8 0

Step-by-step explanation:

Vertical asymptote can be Identites if there is a factor only in the denominator. This means that the function will be infinitely discounted at that point.

For example,

\frac{1}{x - 5}

Set the expression in the denominator equal to 0, because you can't divide by 0.

x - 5 = 0

x = 5

So the vertical asymptote is x=5.

Disclaimer if you see something like this

\frac{(x - 5)(x + 3)}{(x - 5)}

x=5 won't be a vertical asymptote, it will be a hole because it in the numerator and denominator.

Horizontal:

If we have a function like this

\frac{1}{x}

We can determine what happens to the y values as x gets bigger, as x gets bigger, we will get smaller answers for y values. The y values will get closer to 0 but never reach it.

Remember a constant can be represent by

a \times  {x}^{0}

For example,

1 = 1 \times  {x}^{0}

2 =  2 \times {x}^{0}

And so on,

and

x =  {x}^{1}

So our equation is basically

\frac{1 \times  {x}^{0} }{ {x}^{1} }

Look at the degrees, since the numerator has a smaller degree than the denominator, the denominator will grow larger than the numerator as x gets larger, so since the larger number is the denominator, our y values will approach 0.

So anytime, the degree of the numerator < denominator, the horizontal asymptote is x=0.

Consider the function

\frac{3 {x}^{2} }{ {x}^{2}  + 1}

As x get larger, the only thing that will matter will be the leading coefficient of the leading degree term. So as x approach infinity and negative infinity, the horizontal asymptote will the numerator of the leading coefficient/ the leading coefficient of the denominator

So in this case,

x =  \frac{3}{1}

Finally, if the numerator has a greater degree than denominator, the value of horizontal asymptote will be larger and larger such there would be no horizontal asymptote instead of a oblique asymptote.

You might be interested in
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).21,42,84,...Find the 7th term.
Julli [10]

Answer:

21,42,84,168,336,672, 1,344

Step-by-step explanation:

The pattern is to multiply the previous term by 2 to find the next term. The seventh term should be 1,344.

4 0
3 years ago
Read 2 more answers
An investment advisor believes that there is a 60% chance of making money by investing in a specific stock. If the stock makes m
inessss [21]

Answer:

\mathbf{ 0.6 \times 0.5 = 0.3 }

Step-by-step explanation:

Let M denote the event that the stock makes money and D denote the event that the stock pays dividends.

It is given that P(M) = 0.6

Observe that the two events M and D are not independent because if the stock doesn't make money then it will not pay dividends. Therefore the event D | M^{c} (D given M does not occur) is a null event, i.e

P(D|M^{c}) = 0

It is also given that,

P(D|M) = 0.5

Recall that : P(D|M) = \frac{P(D \cap M)}{P(M)}

Here, we are required to find P(D \cap M)

P(D \cap M) =P(D|M) \times P(M)= 0.5 \times 0.6 = 0.3

7 0
3 years ago
Solve negative one equals negative two v plus two-thirds for v.
makkiz [27]
We write it out as an equation:

-1 = -2v + 2/3

Rearrange:
-1 -2/3 = -2v

Multiply by negative to equal positive
1 2/3 = 2v

Make 1 into a fraction
3/3 + 2/3 = 2v
5/3 = 2v
10/6 = 2v
5/6 = v

The answer is: v equals 5/6
3 0
2 years ago
Average winter temperatures in 45 states were recorded and divided by geographic region. Choose True or False for each statement
san4es73 [151]

Answer: SU, TU, ST is the right answer

Step-by-step explanation: In a triangle

The largest side and the largest angle are opposite to each other

The shortest side and the shortest angle are opposite to each other.

So using the above axioms we can observe the triangle.

The largest angle is m∠U = 80° so the side opposite to it is the largest i.e. ST is the largest

The smallest angle is m∠T = 25° so the shortest side is SU

The third side will be the middle side as the angle ∠S is greater than 25° and less than 80°

So the sides in order from least to greatest are: SU, TU, ST

5 0
3 years ago
The graph shows the number of pages to read after x days. Answer the 4 points
yanalaym [24]

Answer:

Step-by-step explanation:

•y-intercept is the 200 pages she has to read to begin with

•x-intercept on day 16 means she has finished reading all the pages, there are

zero pages left

•there are 100 pages left after 8 days

• the line is straight (no change in slope) so the reading rate was consistent over the 16 days.

7 0
2 years ago
Other questions:
  • (10times6)+((17-4)times6)
    11·2 answers
  • A game involves rolling a number cube. You get one point if you roll an even number and negative one point if you roll an odd nu
    10·2 answers
  • What is Radical 84/Two radical three
    15·1 answer
  • ..........................
    6·1 answer
  • Jennifer and Taylor are running together. Taylor thinks Jennifer runs a little slow, so she gives Jennifer a 1 km advantage. Thi
    6·1 answer
  • You buy a shirt for $19.95 and a pair of shorts for $35.95. Shirts are on sale for 25% off and shorts are on sale for 30% off. W
    15·1 answer
  • A grocery store charges $2,49 per pound for organic apples. What is the cost c, in dollars, of p pounds of
    12·1 answer
  • The price of the AC unit with tax is $2,350. If she can save $115 per month, how long will it take to save up for the air condit
    13·1 answer
  • Which biogeochemical cycle is not reliant upon decomposers?
    10·2 answers
  • 23.96448 to the nearest tenth
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!