What is the asymptote of the following function: Y = e^x-x
Answers
Answer:
y = -x
Step-by-step explanation:
Breaking down the equation
[tex]y=e^x-x[/tex] can be written as [tex]y=e^x + (-x)[/tex], making it more clear that this function is composed of two functions:
An exponential function, and a linear functionasymptotes of the parts
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 [tex]e^{-x}[/tex] is equivalent to [tex]\dfrac{1}{e^x}[/tex], 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).
Clarifications
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.
Related Questions
The tables represent the functions f(x) and g(x). f(x) -5 -2 -1 0 1 2 -3 -1 1 3 w 5 X -3 -2 -1 0 1 2 g(x) -13 -9 -5 -1 3 7 Which input value produces the same output value for the two functions? x = -3 O x = -1 x = 0 Ox=1 The tables represent the functions f ( x ) and g ( x ) . f ( x ) -5 -2 -1 0 1 2 -3 -1 1 3 w 5 X -3 -2 -1 0 1 2 g ( x ) -13 -9 -5 -1 3 7 Which input value produces the same output value for the two functions ? x = -3 O x = -1 x = 0 Ox = 1
Answers
Answer:
x=1
Step-by-step explanation:
There are two functions (f & g), each of which have a table of inputs and outputs. The same list of inputs is given to both functions, but the outputs are different.
Imagine that you asked your Father 6 questions, (weirdly instead of numbered 1 through 6, numbered -3 through 2), and that he gave you a list of answers.
Imagine that you asked your Grandfather the same 6 questions, and you got a list of answers from him.
On which question did they give the same answer?
It was on question number "1", (really the 5th question, but as we've numbered things from -3 to 2, it's question "1").
Since the "questions" were the input, "x", x=1.
There are two approaches to solving the equation -3x + 10 = 4x - 20
Subtract 4x from both sides. OR Add 3x to both sides.
–7x + 10 = –20 OR 10 = 7x – 20
Solve the equation using both approaches.
Answers
What is the nth term rule of the linear
sequence
below?
1, 7, 13, 19, 25, . ..
Answers
Answer:
Un= 1+(n-1)6
Step-by-step explanation:
a = 1
d= 7-1= 13-7= 6
and using the formula, Un= a+(n-1)d
Please can someone help asap thank you !x
Answers
Answer:
Step-by-step explanation:
Gradient is the slope, the rise over run, change in y over change in x.
For line A
6/3=2
Gradient=2
For Line B
5/5 =1
Gradient =1
Answer:
•The coordinates of line A (0,1) and (1,3)
gradient formula : y2-y1/x2-x1
gradient :
3-1/1-0=2
Actually you can take any other coordinates for reference!
example :
the other coordinates of line A (0,1) and (2,5)
=5-1/2-0
=2 (same)
•The coordinates of line B (3,2) and (4,1)
Gradient : =1-2/4-3
=-1
or
the coordinat B =(7,-2) and (-2,7)
=7-(-2)/-2-7
=9/-9
=-1
Note:The line to the right has a positive gradient, and the line to the left has a negative gradient
Calculate the unpaid balance, finance charge, and new balance using the unpaid balance method. Note: Interest rate is given as a monthly rate
Previous balance:$179.32
Payments/credits:$85.00
Unpaid balance:$
Monthly rate:1.25%
Finance charge:$
New purchases=$117.42
New balance=$
Answers
The Unpaid balance is $94.32, Finance charge is $1.179 and new balance is $148.079.
Finance charge
Unpaid balance:
Unpaid balance=Previous balance-Payments/credits
Unpaid balance=$179.32-$85.00
Unpaid balance= $94.32
Finance charge:
Finance charge =Finance charge×Monthly rate
Finance charge=$94.32×1.25%
Finance charge=$1.179
New balance:
New balance =Previous balance-(New purchases-Payments/credits)+Finance charges
New balance=$179.32-($117.42-$85.00)+$1.179
New balance=$179.32-$32.42+$1.179
New balance=$148.079
Therefore the Unpaid balance is $94.32, Finance charge is $1.179 and new balance is $148.079.
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Answer:
94.32
1.18
212.92
in order
Step-by-step explanation:
How would i find the domain of this?
Answers
The domain of the graph is {x : x∈ R}
How to determine the domain?The domain of a function or graph is the set of input values the function can take.
This in other words represents the x values
From the graph, we can see that x values extend indefinitely on both axes.
This is indicated by the arrows at the ends of the curve
This means that the domain is the set of all real numbers
Hence, the domain of the graph is {x : x∈ R}
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good afternoon can someone please helppp :))))
Triangle XYZ is dilated by a scale factor of 1/4 to form triangle X'Y'Z'. Side YZ measures 18. What is the measure of side Y'Z'?
(Round your answer to the nearest tenth)
Answers
CD is the perpendicular bisector of both XY and ST, and CY = 16. Find TY.
Answers
The value of TY is 14
Given that CD is the perpendicular bisector of XY and ST and CY = 16
We need to find the value of TY
Here M is the midpoint of ST and D is the midpoint of XY
As shown in the diagram we can say that
CT = CS =12
We can also say that ST║XY
So , ∠CST = ∠CSY
∠CTS = ∠CYX
ΔSCT = ΔXCY
SX = CS - CX
= CY - CX
We can say that MT = SM = 5
DY = DX = 7
TY = SX = 4
CY = CX = 16
ST = SM + MT
ST= 5+5
∴ ST= 10
XY = XD +DY
XY = 7+7
∴ XY = 14
Hence the value of XY is 14
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Find a pattern for the sequence. Use the pattern to show the next two terms.
12, 24, 36, 48, . . .
A. Each term is twelve more than the preceding term; 60, 72
B. Each term is twice the preceding term; 72, 96
C. Each term is five times the preceding term; 60, 70
D. Each term is twelve times the preceding term; 60, 72
Answers
Answer:
about this question the sequence of the pattern is according to the table of 12.
Step-by-step explanation:
Table of twelve is.
12
24
36
48
then the answer will be 60
is 8.6 a rational number
Answers
Answer:
Yes
Step-by-step explanation:
Yes, 8.6 is a rational number because it can be expressed in the form of p/q
[tex]8.6 = \frac{86}{10} = \frac{43}{5} [/tex]
The slope of the line below is -4. Which of the following is the point-slope
form of the line?
(2,-8)
Answers
Answer:
y+2= -4(x-8)
Step-by-step explanation:
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 8x and y = 2x + 2 intersect are the solutions of the equation 8x = 2x + 2. (4 points)
Part B: Make tables to find the solution to 8x = 2x + 2. Take the integer values of x between −3 and 3. (4 points)
Part C: How can you solve the equation 8x = 2x + 2 graphically? (2 points)
Quickly please! Thank you.
Answers
The point of intersection of two given equations is (0.333, 2.667).
Given that, equation with two variables are y = 8x and y = 2x + 2.
The given equations will intersect at some point where y is the same for both equations.
When you replace y in y = 2x + 2 with y = 8x, we get 8x = 2x + 2.
So, the solution of 8x = 2x+2 will satisfy both equations.
Now, we need to find the solutions to take the integer values of x between -3 and 3.
That is,
x = -3 , then 8(-3) = 2(-3) +2⇒-24 = -6+2
⇒-12 = -4 False.
similarly, for x = -2
8(-2) = 2(-2)+2
⇒-16 = -2 False
For, x = -1
8(-1) = 2(-1)+2
⇒-8= 0 False
For, x = 0
8(0) = 2(0)+2
⇒0= 2 False
For, x = 1
8(1) = 2(1)+2
⇒8= 4 False
For, x = 2
8(2) = 2(2)+2
⇒16 = 6 False
For, x = 3
8(3) = 2(3)+2
⇒24 = 8 False
Therefore, there is no solution to 8x = 2x +2 for the integers values of x between -3 and 3.
The equations can be solved graphically by plotting the two given functions on a coordinate plane and identifying the point of intersection of the two graphs.
The point of intersection is the values of the variables which satisfy both equations at a particular point.
Hence, you can see the graph as shown below, the point of intersection is (0.333, 2.667).
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Which table represents a linear function?
Answers
Answer:
1st one.
Step-by-step explanation:
Three teachers shared 4/5 of a flat paper that was donated to the school. what fraction of the flat paper did each teacher receive
Answers
Evaluate the expression (8×6) +(8-3)
Answers
Answer:
(8×6)+8-3
48+8-3
53
Step-by-step explanation:
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the amount a gardener gets paid is directly proportional to the number of hours it takes for him to complete the job.
the gardener got paid £70 for a 12 hour job.
how much would he get paid for a job that took a total of 18 hours?
Answers
Answer:
£105
Step-by-step explanation:
The pay is proportional to the time, so working 18/12 = 3/2 times as long will gain the gardener 3/2 times the pay:
3/2 × £70 = £105
He would get paid £105 for an 18-hour job.
__
Here are a couple of other solution methods.
as a proportionpay/hours = ?/(18 hours) = £70/(12 hours)
Multiplying by 18 hours, we get ...
? = £70×(18 hours)/(12 hours) = £70×(18/12)
? = £105 . . . . pay for 18 hours
He would get paid £105 for 18 hours.
__
as direct proportion equationThe equation for a directly proportional relationship is ...
y = kx
If we let y represent pay and x represent hours, then we have ...
70 = k(12) ⇒ k = 70/12 = 35/6
Then for 18 hours, the pay is ...
y = (35/6)x
y = (35/6)(18) = 35(3) = 105
He would get paid £105 for 18 hours.
Solve the following equations. 2x - y = 8 3x + y = 17
Answers
System of equations:
2x - y = 8
3x + y = 17
Solve for x:2x - y = 8
3x + y = 17
________ +
5x = 25
x = 5
Plug in x to one of the equations to solve for Y2(5) - y = 8
10 - y = 8
-y = -2
y = 2
Expand . ( 3x –2 ) 2 need an answer ASAP.
Answers
Answer:
6x - 4
Step-by-step explanation:
For expanding (3x -2) 2 , (3x - 2) is to be multiplied with 2.
(3x - 2) × 2 = 6x - 4
Describe the varying vegetation regions in Canada
Answers
Answer:
es fácil solo tienes que Aser 23+578 y hay te da el resultado
Figure A
Figure B
Figure A is rotated 180°, then reflected across the line.
Figure B is reflected across the line, then rotated 180°.
Which of the following shows the two figures after they are
transformed?
Answers
Answer:
The answer is c
Step-by-step explanation:
look at the picture carefully
3. Find x 75° (4x 25)°
Answers
If two lines intersect, then their opposite angles are equal. Then the value of x is 25°.
The missing graph is given below.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
Vertically opposite angle - When two lines intersect, then their opposite angles are equal.
Then the value of x will be
75° = (4x - 25)°
100° = 4x
x = 25°
Then the value of x is 25°.
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Ryan invested $5000 in an account that averaged 5% growth per year. Which equation would be used to best model the situation?
Answers
Answer:
f(x)=5000(1+0.05)^x
Step-by-step explanation:
Use the formula: f(x)=P(1+b)^x
P is principal or y-intercept. 5000 is principal.
b is the percentage in decimal form. 0.05 is b.
x is time, in this case years. Since there is not a certain number of years leave x as x.
f(x)=5000(1+0.05)^x
Hope this helps!
If not, I am sorry.
How many real solutions does the system of equations have? y = x2 + x − 2 y = -x + 1
Answers
The number of the solutions of the equations are 2 that are (1, 0) and (-3, 4).
What are the solutions of the equations?The equations are given below.
y = x² + x − 2 ...1
y = – x + 1 ...2
From equations 1 and 2, we have
x² + x − 2 = – x + 1
x² + 2x − 3 = 0
Then the factor of the equation will be
x² + 3x – x − 3 = 0
(x + 3)(x – 1) = 0
x = 1, –3
Then the value of y will be
At x = 1, we have
y = -1 + 1
y = 0
At x = -3, we have
y = -(-3) + 1
y = 4
Then the number of the solutions of the equations are 2 that are (1, 0) and (-3, 4).
The graph is given below.
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Which figure has two circular faces?
Figure A
O figure A
Ofigure B
figure C
figure D
Figure B
Figure C
Figure D
Answers
A cylinder is a 3D shape having two circular faces.
The answer is Figure A
a candy bar is in the shape of a triangular prisim the volume of the box is 2400 cubic centimeters. what is the height of the base
Answers
The height of the base will be 15 cm. The candy bar has a 2400 cubic centimeter box with a triangular prism form to it.
What is the definition of a triangular prism?Join the edges of three rectangles. Now, from both ends, seal their triangle mouths. A triangular prism is a name for the form.
The complete question is;
"A candy bar is in the shape of a triangular prism the volume of the box is 2400 cubic centimeters. It is shown with a base of the triangle labeled 16 cm, the sides of triangles labeled 17 cm, and the length of the box equal to 20 cm. what is the height of the base triangular prism"
The volume of the triangular prism;
[tex]\rm V = \frac{1}{2}\times b \times h\times l\\\\ 2400 \ cm^3 = \frac{1}{2}\times 16 \ cm \times h\times 20 \ cm \\\\ h = 15 \ cm[/tex]
Hence, the height of the base will be 15 cm.
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A circle has a diameter with endpoints (-7, 1) and (-3, 7).
What is the equation of the circle?
r2 = ( x - 3) 2 + ( y + 4) 2
r2 = ( x + 3) 2 + ( y - 4) 2
r2 = ( x + 5) 2 + ( y - 4) 2
r2 = ( x - 5) 2 + ( y + 4) 2
Answers
Answer: (C) r² = (x+5)²+(y-4)²
Solution:-
The given endpoints are (-7,1) and (-3,7)
so the center will be at the mid point of the line connecting these two points.
hence, center ={ (-7+-3)/2, (1+7)/2 }
hence, C= (-5,4)
so, the equation of the circle is:-
⇒ (x-(-5))²+(y-4)²=r²
or, (x+5)²+(y-4)²=r²
How many significant digits are there in the number 237.16?
Answers
Answer:
3
Step-by-step explanation:
simplify the equation. 3(x+2)-9x+5
Answers
Distribute
3(x + 2) - 9x + 53x + 6 - 9x + 5Add the numbers
3x + 6 - 9x + 53x + 11 - 9xCombine like terms
3x + 11 -9x-6x + 11Distribute
3(x + 2) - 9x +5
3x + 6 - 9x + 5
Add the numbers
3x + 6 - 9x + 5
3x + 11 - 9x
Combine like terms
3x + 11 - 9x
6x + 11
4. Write an equation that describes the verbal description. Then, explain your thinking.
Teddy opens a new bank account by depositing the $245 he has saved from mowing lawns. He chose
this account because it will accrue 2% monthly and he wants to save up $2,000 for a car within a
couple of years.
P
Answers
Answer:
245 +4.9m = 2000
Step-by-step explanation:
so 245 is what he has and he puts it where he gets 2 percent monthly so 4.9 is 2 percent of 245. 2000 is there because that's how much he wants to save.
8. Scott drank 3.5 bottles of water yesterday. Each bottle contained 1.2 pints of water. What was the number of pints of water Scott drank yesterday? Ascend Learning 8. Scott drank 3.5 bottles of water yesterday . Each bottle contained 1.2 pints of water . What was the number of pints of water Scott drank yesterday ? Ascend Learning
Answers
Answer:
4.2 pints
Step-by-step explanation:
3.5 × 1.2 = 4.2
Answer: 4.2 pints