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} ...
If I zoom in on the origin, I can also see that the graph crosses the horizontal asymptote (at the arrow): It is common and perfectly okay to cross a horizontal asymptote. (It's the vertical asymptotes that I'm not allowed to touch.) ...
Question: Use the graph shown to find the following.(a) The domain and range of the function(b) The intercepts, if any(c) Horizontal asymptotes, if any(d) Vertical asymptotes, if any(...
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 ...
Consider the function, f(x) = 3(x+1)-9 i) State the domain and range of f(x). ii) State all the x-, y-intercept(s), horizontal and vertical asymptote(s), if any, of the graph of f(x). iii) Given that f i Consider g(x) = (x+1)^2/1+x^2. (a) Fin...
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 left of the y-axis it crosses at x equals ...