Find the horizontal asymptote of: y = \frac{e^x}{2e^{x + 5 How do you determine if a graph crosses a horizontal asymptote? Find the horizontal asymptote, if any, of the graph of the rational function. g (x) = {12 x^2} / {3 x^2 + 1} ...
The graph shows that there's some slightly interesting behavior in the middle, right near the origin, but the rest of the graph is fairly boring, trailing along the x-axis. If I zoom in on the origin, I can also see that the graph crosses the horizontal asymptote (at the arrow): It...
The slant (or oblique) asymptote for that rational function is a straight (but not horizontal or vertical) line that shows where the graph goes, off to the sides.How do you find the slant (or oblique) asymptote?To find the slant asymptote, do the long division of the numerator by the ...
Find the oblique asymptote (if there is any) for the function (x^2 + 7x + 4)/(x + 5) and find the vertical asymptote (if there is any) for the function f(x)= (x - 1)/(x^2 + 9). Use a graphing utility to graph the function and determine the ...
Determine the asymptotes if has. Graph the function. Find the domain, range, and asymptote. h(x) = 7 - 5^x Consider the function f (x) = x^2 + 1 / x + 1. (a) State the domain of the function. (b) Identify all intercepts. (c) Find any vertical and horizontal as...
There’s something else here that is interesting. Let’s look at where the graph touches the x-axis. It crosses at x = 0 and to the right it crosses again a bit after 3 and a bit more after 6. If we were to zoom in we would see that it crosses at pi and two pi! To the ...