SOLUTION: Basic question. f(x) equals y because plugging in some value x into the function will give you what the corresponding y-value will be. And the y-value of a LINEAR FUNCTION will alw
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Question 1001042: Basic question. f(x) equals y because plugging in some value x into the function will give you what the corresponding y-value will be. And the y-value of a LINEAR FUNCTION will always be the same thing as its horizontal asymptote?
I know the function will output differently for a rational function, and then the rules change. but for something like lim x -> ∞ where the function is f(x) = 5+e^(-x^2). By plugging in ∞ into the function this will output the horizontal asymptote because the horizontal asymptote is the same as y-value. In this case y = 5 and that is the horizontal asymptote.
not sure if this is right or not.
Please help! Answer by ikleyn(52790) (Show Source):
You can put this solution on YOUR website! .
Below is the plot of the functions y1 = (in red) and y2 = (in green) with the horizontal asymptote y = 5 (in blue).
Figure. Plots y1 = and y2 =
The function y2 = tends to zero at x ---> +/-.
Therefore, the function y1 = tends to 5 at x ---> +/-.
y = 5 is the horizontal asymptote for the function y1.
Notice that the function y1 is not a rational function, as well as the function y2.
