To find a slant (or oblique) asymptote, long-divide the numerator by the denominator; ignore the remainder. The polynomial part is your asymptote.
Step 3:Find any horizontal asymptotes by examining the end behavior of the graph. A horizontal asymptote is a horizontal liney=dthat the graph of the function approaches asxgets really large or really small. Step 4:Determine the domain by looking at the graph fro...
no matter what the base is (this is called the locator point); the asymptote will be one unit to the left of the locator pt.: y-axis The h value moves the entire graph : right if h is positive, left if h is negative The k value moves the entire graph : up if k is positive...
Set each factor in the denominator equal to zero and solve for the variable. If this factor does not appear in the numerator, then it is a vertical asymptote of the equation. If it does appear in the numerator, then it is a hole in the equation. In the example equation, solving x –...
Find the horizontal asymptote of the following function: First, notice that the denominator is a sum of squares, so it doesn't factor and has no real zeroes. In other words, this rational function has no vertical asymptotes. So we're okay on that front. ...
The sine and cosine functions do not have vertical asymptotes. They are defined at all real numbers. To find vertical asymptotes for the other four...Become a member and unlock all Study Answers Start today. Try it now Create an account Ask a question Our experts can answer your tough...
it has a vertical asymptote. Once you've written out your function, find the value of x that makes the denominator equal to zero. As an example, if the function you're working with is y = 1/(x+2), you would solve the equation x+2 = 0, an equation which has the answer x = ...
How to find vertical asymptotes f(x) = 2x2 3x find vertical asymptote(s). Find the vertical asymptotes, if any: f(x) = (x + 2)/(x^2 - 4). Find all vertical asymptotes of f(x)=e^x 3e^x-4 . Find vertical asymptotes, if any of f(x) = \frac{x^3 - 10x^2 + 16x}{x...
it has a vertical asymptote. Once you've written out your function, find the value of x that makes the denominator equal to zero. As an example, if the function you're working with is y = 1/(x+2), you would solve the equation x+2 = 0, an equation which has the answer x = ...
Steps to graph a function When graphing functions, we take the following steps: Find the function’s domain and range and keep them in mind as you draw the curve. Find and plot the x-intercept(s) and y-intercept(s). Determine whether or not there are any holes. Find the asymptotes ve...