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
Alex787 [66]
3 years ago
5

Which type of asymptote, when it occurs, describes the behavior of a graph when x is close to some number?

Mathematics
1 answer:
arsen [322]3 years ago
4 0
Answer: A slant or oblique asymptote.

Explanation:
When a function is a rational function whose denominator is one degree lower than the numerator, a slant or oblique asymptote occurs when the function is graphed.

Example:
Consider the rational function
y = (2x² + 2x + 3)/(x + 1)
The degree of the numerator is 2, and the degree of the denominator is 1 so that the degree of the numerator is one higher than that of the denominator.

After long division, obtain
                    2x
       -----------------------
x+1  |  2x²  + 2x  + 3
          2x²  + 2x
         -------------------
                             3

That is,
(2x²+2x+3)/(x+1) = 2x + 3/(x+1)
As x -> ∞, 3/(x+1) -> 0, and the curve behaves as the straight line y = 2x.
The curve, therefore, approaches the straight line with a slope of 2.
For this reason, it is called a slant or oblique asymptote.

The graph of this function is shown below to illustrate the concept.

You might be interested in
Solve the system of linear equations by elimination.<br><br> 4x−3y=8<br> 5x−2y=−11
AleksandrR [38]

Answer:

(-7, -12)

Step-by-step explanation:

4x-3y=8

5x-2y=-11

Is there any of the like terms can be added and the result will be 0? No, so we have to multiple one OR both of the equations to make that one number do that.

(I will try to remove the y like terms so i will multiple both of them by the opposite so both of the ys will be 6)

2(4x-3y=8)

-3(5x-2y=-11)

8x-6y=16

-15x+6y=33

(now the easy part… cancel the 6s and add the equations)

8x+(-15x)=-7x

16+33=49

-7x=49

(divide 49 by -7)

x=-7

Replace x in any of the equations and you’ll get the y value.

4x-3y=8

4(-7)-3y=8

-28-3y=8

-3y=36

y=12

Threfore, there is one solution which is….. (-7,-12)

7 0
2 years ago
A distribution has a mean of 16 and a standard deviation of 6. What is the Z score that corresponds with 34?
Brrunno [24]

Answer:

Z = 3

Step-by-step explanation:

In a normal distribution, the Z score that corresponds with a data point x is calculated using the formula;

Z=\frac{x-mean}{standard deviation}

For the case given, the z score will be;

Z=\frac{34-16}{6}=3

7 0
3 years ago
Write an algebraic expression to answer the question below. if 10 calculators cost d dollars, how much, in dollars, does each ca
kupik [55]
It should cost 8 dollars all together.
4 0
3 years ago
What is the value of the expression 8 cubed?
Ierofanga [76]

Answer:

512

Step-by-step explanation:

8*8*8

64*8

512

5 0
3 years ago
Read 2 more answers
On Saturday, local hamburger shop sold a combined total of 380 hamburgers and cheeseburgers. The number of cheeseburgers old was
Mrac [35]

Answer:

95 hamburgers

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Other questions:
  • Tim answered all queston on is math test but got 10 answers wrong. He received 4 points for every corect answer, and there was n
    14·1 answer
  • PLLLSSSSSS HURRRYYYY To convert Celsius temperatures to Fahrenheit, you can use the expression 9/5 (C + 32). Tom says that anoth
    5·1 answer
  • If a storm window has an area of 448 square inches, what are the dimensions if the window is 12 inches higher than it is wide (w
    5·2 answers
  • What is 8 3/8 - 6/8 =
    12·2 answers
  • The results of a swim meet are shown. Who swam the fastest? Explain Your Reasoning. Tawni- 50-m-Freestyle Time= 40.8 Pepita-100-
    9·1 answer
  • A cell phone plan has a monthly cost that is shown in the table below. What is the correct statement regarding the average rate
    11·1 answer
  • Question 1. When solving the equation 10 = x + 3 what should you do to both sides of the equation? o add 3 O subtract 3 O multip
    13·2 answers
  • A game spinner is divided into 5 congruent sections and labeled, as shown below.
    7·1 answer
  • What is 6 in 16.5 rounded to
    15·1 answer
  • What are the new coordinates of L' if the following image has a dilation of 1/2?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!