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Anastaziya [24]
2 years ago
7

What is the asymptote of the following function: Y = e^x-x

Mathematics
1 answer:
N76 [4]2 years ago
5 0

Answer:

y = -x

Step-by-step explanation:

<u>Breaking down the equation</u>

y=e^x-x can be written as y=e^x + (-x), making it more clear that this function is composed of two functions:

  • An exponential function, and
  • a linear function

<u>asymptotes of the parts</u>

The regular exponential function normally has an asymptote at y=0, a horizontal line because as "x" gets more and more negative, e^(x) gets closer and closer to zero (see blue graph).  This asymptotic behavior perhaps can be more easily understood by recognizing that e^{-x} is equivalent to \dfrac{1}{e^x}, so that as the x values get more and more negative, it is effectively dividing 1 by a larger and larger number, thus getting closer and closer to zero.

In this situation, that exponential function is added to "-x", which is a linear function with a slope of negative 1.

As the left end of the exponential function gets closer and closer to zero, the exponential part contributes almost nothing to the sum, whereas as the "x" gets more and more negative, the linear function "-x" gets more and more positive (linearly).  Since the exponential piece adds almost nothing to it (when moving to the left), the combined function is essentially "-x" (although it is ever so slightly greater than it, just as it was ever so slightly greater than zero) (see pink graph, with dashed asymptote).

<u>Clarifications</u>

To be clear, on the right side of the graph, the exponential part of the function completely overwhelms the linear piece, and the function behaves much more like an exponential function, nearly completely masking the behavior of the linear piece.  Since an exponential function is unbounded, and the domain of both the exponential and linear functions are all real numbers, on the right side of the graph, there is no asymptotic behavior.

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svetlana [45]

Answer:

Linear Pair:

∠ 1 and ∠ 2

Vertical Angles:

∠ 1 and ∠ 3

Supplementary Angles:

∠ 7 and ∠ 6

Step-by-step explanation:

Linear Pair:

A linear pair of angles is formed when two lines intersect.

Two angles are said to be linear if they are adjacent angles formed by two intersecting lines.

The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

Example

∠ 1 and ∠ 2           ∠ 8 and ∠ 5 ,etc

Vertical Angles:

The angles opposite each other when two lines cross.

They are always equal.

Example

∠ 1 and ∠ 3           ∠ 8 and ∠ 6 ,etc

Supplementary Angles:

Two Angles are Supplementary when they add up to 180 degrees.

Examples  two angles (140° and 40°)

All Linear pair are Supplementary angles

Example

∠ 7 and ∠ 6           ∠ 8 and ∠ 5 ,etc

3 0
3 years ago
Use the associative property to simplify the expression.
BaLLatris [955]

Answer:

the answer is 143 cus u add throw

through

3 0
2 years ago
Read 2 more answers
Please help me! :) !!!!!!!!!!!!!!!!!
Novosadov [1.4K]

Answer:

x=17

Step-by-step explanation:

Since the triangles are congruent, the angles are equal

I≅ P  

3x+4 = 72-x

Add x to each side

3x+4+x = 72-x+x

4x+4 = 72

Subtract 4 from each side

4x+4-4 = 72-4

4x= 68

Divide by 4

4x/4 = 68/4

x = 17


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3 years ago
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slavikrds [6]
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3 years ago
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Pavel [41]
I you're looking for the equation, it is 

x+25  \ \textless \  75

and If you need me to solve it, it is 

x \ \textless \  50
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