06:41Finding All Asymptotes of a Rational Function (Vertical, Horizontal, Oblique / Slant)patrickJMT365views1rank
07:52Rational Function : Find the Asymptotes (Vertical, Horizontal, Slant / Oblique)patrickJMT404views2rank
02:17Vertical Asymptotes of Rational Functions: Quick Way to Find Them, Another Example 1patrickJMT407views
02:07Vertical Asymptotes of Rational Functions: Quick Way to Find Them, Another Example 2patrickJMT509views
04:08Find the Equations of the Vertical and Horizontal Asymptotes of Rational Function f(x)=(3x+12)/(x+2)Wendy1157views
Multiple ChoiceSketch the graph of the function f(x)=1x2f\left(x\right)=\frac{1}{x^2}f(x)=x21. Identify the asymptotes on the graph.193viewsHas a video solution.
Multiple ChoiceBased only on the vertical asymptotes, which of the following graphs could be the graph of the given function? f(x)=x2−4xx2−x−12f\left(x\right)=\frac{x^2-4x}{x^2-x-12}f(x)=x2−x−12x2−4x139viewsHas a video solution.
Multiple ChoiceFind all vertical asymptotes and holes of each function. f(x)=−5x(2x−3)2f\left(x\right)=\frac{-5x}{\left(2x-3\right)^2}f(x)=(2x−3)2−5x124viewsHas a video solution.
Multiple ChoiceFind all vertical asymptotes and holes of each function. f(x)=x2−2x2x3−x2−6xf\left(x\right)=\frac{x^2-2x}{2x^3-x^2-6x}f(x)=2x3−x2−6xx2−2x149viewsHas a video solution.
Multiple ChoiceFind all vertical asymptotes and holes of each function. f(x)=x2+10x+252x2+8x−10f\left(x\right)=\frac{x^2+10x+25}{2x^2+8x-10}f(x)=2x2+8x−10x2+10x+25151viewsHas a video solution.
Multiple ChoiceFind the horizontal asymptote of each function. f(x)=−5x(2x+3)2f\left(x\right)=\frac{-5x}{\left(2x+3\right)^2}f(x)=(2x+3)2−5x164views2rankHas a video solution.
Multiple ChoiceFind the horizontal asymptote of each function. f(x)=8x2+12x2−x−6f\left(x\right)=\frac{8x^2+1}{2x^2-x-6}f(x)=2x2−x−68x2+1122viewsHas a video solution.
Multiple ChoiceFind the horizontal asymptote of each function. f(x)=x2+4x2x3+8x2f\left(x\right)=\frac{x^2+4x}{2x^3+8x^2}f(x)=2x3+8x2x2+4x151viewsHas a video solution.
Textbook QuestionIn Exercises 1–8, find the domain of each rational function. f(x)=5x/(x−4)190viewsHas a video solution.
Textbook QuestionIn Exercises 1–8, find the domain of each rational function. g(x)=3x^2/(x−5)(x+4)237viewsHas a video solution.
Textbook QuestionIn Exercises 1–8, find the domain of each rational function. h(x)=(x+7)/(x^2−49)245viewsHas a video solution.
Textbook QuestionUse the graphs of the rational functions in choices A–D to answer each question. There may be more than one correct choice. Which choices have domain (-∞, 3)U(3, ∞)?158viewsHas a video solution.
Textbook QuestionUse the graph of the rational function in the figure shown to complete each statement in Exercises 9–14. As x -> 1^-, f(x) -> __147viewsHas a video solution.
Textbook QuestionUse the graph of the rational function in the figure shown to complete each statement in Exercises 9–14. As x -> -∞, f(x) -> __410views1rankHas a video solution.
Textbook QuestionUse the graph of the rational function in the figure shown to complete each statement in Exercises 15–20. As x -> 1^+, f(x) -> __286viewsHas a video solution.
Textbook QuestionMatch the rational function in Column I with the appropriate descrip-tion in Column II. Choices in Column II can be used only once. ƒ(x)=(x+7)/(x+1)136viewsHas a video solution.
Textbook QuestionIn Exercises 21–36, find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of each rational function. f(x)=(x^2−9)/(x−3)595viewsHas a video solution.
Textbook QuestionMatch the rational function in Column I with the appropriate descrip-tion in Column II. Choices in Column II can be used only once. ƒ(x)=1/(x+4)120viewsHas a video solution.
Textbook QuestionIn Exercises 21–36, find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of each rational function. g(x)=(x−3)/(x^2−9)193viewsHas a video solution.
Textbook QuestionIn Exercises 21–36, find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of each rational function. h(x)=(x+7)/(x^2+4x−21)198viewsHas a video solution.
Textbook QuestionGive the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. See Example 4. ƒ(x)=(x^2-1)/(x+3)202viewsHas a video solution.
Textbook QuestionGive the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. See Example 4. ƒ(x)=(x^2+4)/(x-1)107viewsHas a video solution.
Textbook QuestionGive the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. See Example 4. ƒ(x)=(x^2-2x-3)/(2x^2-x-10)146viewsHas a video solution.
Textbook QuestionIn Exercises 45–56, use transformations of f(x)=1/x or f(x)=1/x^2 to graph each rational function. h(x)=1/x + 2116viewsHas a video solution.
Textbook QuestionIn Exercises 45–56, use transformations of f(x)=1/x or f(x)=1/x^2 to graph each rational function. g(x)=1/(x+1) − 2125viewsHas a video solution.
Textbook QuestionWork each problem. Choices A–D below show the four ways in which the graph of a rational function can approach the vertical line x=2 as an asymptote. Identify the graph of each rational function defined in parts (a) – (d). ƒ(x)=-1/(x-2)^2108viewsHas a video solution.
Textbook QuestionIn Exercises 45–56, use transformations of f(x)=1/x or f(x)=1/x^2 to graph each rational function. g(x)=1/(x+2)^2134viewsHas a video solution.
Textbook QuestionWork each problem. Which function has a graph that does not have a horizontal asymptote? A. ƒ(x)=(2x-7)/(x+3) B. ƒ(x)=3x/(x^2-9) C. ƒ(x)=(x^2-9)/(x+3) D. ƒ(x)=(x+5)/(x+2)(x-3)106viewsHas a video solution.
Textbook QuestionIdentify any vertical, horizontal, or oblique asymptotes in the graph of y=ƒ(x). State the domain of ƒ. 111viewsHas a video solution.
Textbook QuestionIdentify any vertical, horizontal, or oblique asymptotes in the graph of y=ƒ(x). State the domain of ƒ. 133viewsHas a video solution.
Textbook QuestionGraph each rational function. See Examples 5–9. ƒ(x)=(x+1)/(x-4)133viewsHas a video solution.
Textbook QuestionGraph each rational function. See Examples 5–9. ƒ(x)=3x/(x^2-x-2)147viewsHas a video solution.
Textbook QuestionIn Exercises 57–80, follow the seven steps to graph each rational function. f(x)=(x+2)/(x^2+x−6)99viewsHas a video solution.
Textbook QuestionIn Exercises 57–80, follow the seven steps to graph each rational function. f(x)=(x−2)/(x^2−4)162viewsHas a video solution.
Textbook QuestionSolve each problem. Work each of the following. Find an equation for a possible corresponding rational function.129viewsHas a video solution.
Textbook QuestionSolve each problem. Work each of the following. Find an equation for a possible corresponding rational function.96viewsHas a video solution.
Textbook QuestionIn Exercises 57–80, follow the seven steps to graph each rational function. f(x)=x^4/(x^2+2)141viewsHas a video solution.
Textbook QuestionSolve each problem. Find a rational function ƒ having the graph shown. 150viewsHas a video solution.
Textbook QuestionIn Exercises 89–94, the equation for f is given by the simplified expression that results after performing the indicated operation. Write the equation for f and then graph the function. 5x^2/(x2−4) ⋅ (x^2+4x+4)/(10x^3)112viewsHas a video solution.
Textbook QuestionIn Exercises 89–94, the equation for f is given by the simplified expression that results after performing the indicated operation. Write the equation for f and then graph the function. x/(2x+6) − 9/(x^2−9)141viewsHas a video solution.
Textbook QuestionIn Exercises 89–94, the equation for f is given by the simplified expression that results after performing the indicated operation. Write the equation for f and then graph the function. (1 − 3/(x+2)) / (1 + 1/(x−2))101viewsHas a video solution.