An asymptote is a line to which the graph of a curve is very close but never touches it. There are three types of asymptotes: horizontal, vertical, and slant (oblique) asymptotes. Learn about each of them with examples.
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 function approaches zero, it has...
How does a horizontal asymptote differ from a vertical asymptote?Vertical and horizontal asymptotes differ in the following ways:Whereas vertical asymptotes are sacred ground — which must never be touched — horizontal asymptotes are just useful suggestions. Whereas you can never touch a vertical ...
Graph the rational function f(x)=(-6)/(x-6)To graph the function, draw the horizontal and vertical asymptotes (if any) and plot at least two point the graph. 相关知识点: 试题来源: 解析 x-6=0 x=6 vertical asymptote at x=6 horizontal asymptote at y=0 ...
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...
Find the vertical and horizontal asymptotes of the following rational function. (align*)y = 1/(x^2 + 4x + 3)(align*) 相关知识点: 试题来源: 解析 Vertical asymptotes: (align*)x = -3(align*) and (align*)x = -1(align*) Horizontal asymptote: (align*)y = 0(align*) ...
Therefore, the limit at a vertical asymptote is infinity and a number at a horizontal asymptote if it exists.What is a limit of a function? value A limit of a function is the value the function approaches as x approaches some number. For a continuous function such as polynomial and ...
When x approaches -5/2 from the right (x > -5/2), 9x - 3 < 0, 2x + 5 > 0, f(x) < 0 and approaches negative infinity. So x = -5/2 is its vertical asymptote.When x approaches infinity or negative infinity, the limit of f(x) is 9/2, which is its horizontal asymptote....
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R(x) = (x^3 - 27) / (x^2 - 4x + 3). Find vertical, horizontal, and oblique asymptotes. What is the vertical asymptote of f(x) = \frac{x^3+2}{x+5}? What is the vertical asymptote y=1/(x+6) + 5? What is the horizontal asymptote of y = 2^(x - 1)?