2. What are the vertical asymptotes of this rational function? x = 2 and x = 3 x = 1 and x = 2 x = -2 and x = -3 x = 0 and x = 1 x = 1 and x = -2 Create your account to access this entire worksheet A Premium account gives you access to all lesson, practic...
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...
The intercepts of a function are the values of x when f(x) = 0 and the value of f(x) when x = 0, corresponding to the coordinate values of x and y where the graph of the function crosses the x- and y-axes. Find the y-intercept of a rational function as you would for any o...
Vocabulary for Finding the Intercepts, Asymptotes, Domain, and Range From the Graph of a Rational Function Intercepts:The {eq}x {/eq}-intercept(s) are points at which the graph of the function touches the {eq}x {/eq}-axis. It is possible to have zero, on...
How do you graph a hyperbola?Question:How do you graph a hyperbola?Asymptotes:Asymptotes are invisible lines that the curve of a function gets infinitely close to but never touches. You see asymptotes when graphing parabolas, trig functions and complex rational functions.Answer...
Slant asymptotes are caused by the numerator having a degree that is 1 greater than that of the denominator; they indicate where the graph will be when it's off to the sides. Slant asymptotes can be touched and/or crossed.Find the slant asymptote of the following function: To...
If you have holes, jumps, or vertical asymptotes, you will have to lift your pencil up and so do not have a continuous function.If your function jumps like this, it isn’t continuous.More formally, a function (f) is continuous if, for every point x = a:...
This is because cotangent is undefined at x = nπ since it would require division by zero. At these points, the function has vertical asymptotes. The graph of cotangent has a period of π. For example: cot(0°) = undefined cot(90°) = 0 ...
A start would be to graph the interval and look for asymptotes. Example problem #4 has a discontinuity at x = 9 (at this point, the denominator would be zero, which is undefined) and example problem #5 has a vertical asymptote at x = 2. Therefore, they are both improper integrals. ...
Find a formula for a function that has vertical asymptotes x = 4 and x = 9 and horizontal asymptote y = 4. Determine the horizontal asymptote for the graph of the function f(x) = \sqrt{x^2 + x} - x. How to find horizontal asymptote of xe^x?