as "x" approaches infinity and "y" approaches 0 for the function "y=1/x" — "y=0" is the horizontal asymptote. You can save time in finding horizontal asymptotes by using your TI-83 to create a table of "x" and "y" values of the function, and observing trends in ...
The horizontal asymptote of a function f(x) is defined by the limit {eq}\displaystyle \lim_{x \to \pm \infty} f(x) = k {/eq} If the limit exists... Learn more about this topic: Horizontal Asymptotes | Equations & Examples
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...
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 ...
Domain and Range:The domain of a function is the set of all possible inputsxfor the function. The range of a function is the set of all possible outputsy. We will use these steps and definitions to find the intercepts, asymptotes, domain, and range from the...
Vertical Asymptotes: First Steps To find a vertical asymptote, first write the function you wish to determine the asymptote of. Most likely, this function will be a rational function, where the variable x is included somewhere in the denominator. As a rule, when the denominator of a rational...
From what I know about rational functions and vertical asymptotes (of which, this function has one), I know that the graph will go forever upward and forever downward, so the range is indeed everything other than y = 0. I'll use this to find the domain and range of my inverse. Here...
How do you find the vertical asymptotes of a polynomial? Explain how to locate vertical asymptotes. Find all vertical asymptotes of the function Find the vertical asymptotes of the function f(x) = \frac{x^4 - 4x^3 -x^2 - 4}{2x^3-2} ...
How do you find the slope of asymptotes of a hyperbola? What is the equation of a line that is parallel to y = -4x + 2 and goes through the point (-4, 9)? Find the equation of the tangent line to the graph of y = (2x + 3)/(3x - 2) at the point (1,5) using the qu...
find the x intercept of the equation by setting the value of y to zero and solving the equation. Similarly you can solve the y intercept by setting the value of x to zero and solving the equation. Now while solving this rational function for intercepts if you face a situation where ......