The horizontal asymptote of y = e^x - 1 is y =_________
- print Print
- list Cite
Expert Answers
calendarEducator since 2012
write511 answers
starTop subjects are Math, Science, and Business
An asymptote of a function is a limit the function tends to in either the `x`direction or the `y`direction.
As this is a horizontal asymptote the asymptote is in the `x`direction and is a particular value of `y`.
Look at both ends of the `x`axis, ie when `x`is either very large or very small.
For very large `x`we write `x -> oo`
Since the value of `e` is greater than 1, as `x-> oo` the value of `e^x` also gets very large, that is `e^x -> oo`
and `e^x -1 -> oo` since the magnitude of the -1 term is negligible compared to the size of `e^x`as `x -> oo`.
For very small `x`we write `x -> -oo`
Again since the value of `e` is greater than 1, as `x -> -oo` the value of `e^x` gets very close to zero, that is `e^x -> 0`
and `e^x - 1 -> -1` . This time the magnitude of the -1 term is large compared to the size of `e^x` as `x -> -oo` .
Therefore the horizontal asymptote is y = -1
Related Questions
- What is the double integral of:f(x,y)=e^(x+y) when R is the area bounded by y=x+1, y=x-1, y=1-x,...
- 1 Educator Answer
- The horizontal asymptote of y = (e^x) - 1 is y =?
- 1 Educator Answer
- write a rational function that has a vertical asymptote at x=1, a horizontal asymptote at y=2,...
- 1 Educator Answer
- Find the domain and range of the following: y = x^2 , y = sqrt(1 – x^2), y = 1/x, y = sqrt(x) ,...
- 2 Educator Answers
- ((e^x)+(e^-x))/2=1
- 1 Educator Answer