For the rational function f (x) = x2-1x (x - 2) a. Calculate the equations of...
5. (6 points) Analyze the graph of the rational function f(x) = x + x -12 x² - 4 Label the intercepts, asymptotes, if any.
| Sketch the curve of the function f(x) = + unction f(x) = "* [r'(x) = 2*, S"(x) = 205*] Do this by determining the following information: domain, vertical asymptotes and limit - behavior, horizontal asymptotes, x \& y intercepts, symmetry, intervals of increase/decrease and maximum/minimum points, intervals of concavity and inflection points
5. For the graph of this rational function, state the domain and write the equations of any asymptotes and coordinates of any hole. 4M Domain : Hole : Vertical asymptote(s) : Horizontal Asymptote : 6. For the graph of this rational function, identify the equations of any asymptotes and the coordinates of any hole. f(x) = - 2x + 10 x x? - 25 4M V.A.:
Determine the L- and y-intercepts (if any), and vertical and horizontal asymptotes of the rational function r, given by 3.x2 + 18x + 24 r(x) = x2 – 3x + 2 and then use this information to sketch a graph of r. As part of your analysis, you should explicitly examine the behaviour of the function on both sides of each vertical asymptote, and evaluate the function at appropriate test points.
The graph of a rational function f is shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "holes", Use the graph to complete the following. (a) Write the equations for all vertical and horizontal asymptotes. Enter the equations using the "and" button as necessary. Select "None" as necessary. : None O=o (0,0) Dando Vertical asymptote(s): 1 Horizontal asymptote(s): U [0,0] (0,0) (0,0) O ovo 00 - - -8 EEE-- - -6 1 (b)...
(1) For the function f(x) = −x , identify the intervals of increase/decrease and concave up/down.x2 − 1 Sketch a graph of the function in accordance with these conditions. Your sketch should also include • the following points: the x and y intercepts, local maximums, local minimums, and inflections, • and all asymptotes (both horizontal and vertical). If the function does not have a property listed above, then clearly state that the function does not satisfy the requested property. (2)...
3x Determine whether f(x)-is rational is a rational function and state its domain. Is f a rational function? OA. Yes O B. No What is the domain of f? Select the correct choice below and, if necessary, fill in the answer box to complete your choice Type an integer or a fraction. Use a comma to separate answers as needed.) Type an integer or a fraction.) (Type an integer or a fraction.) O D. The domain is all real numbers....
Give the equations of any vertical asymptotes for the graph of the rational function. (x+4)(x-7) f(x) = (x - 5)(x-7) Select the correct choice below and fill in any answer boxes within your choice. O A. The vertical asymptote is x = (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) OB. There is no vertical asymptote.
7. Given f(x)=_x - 2x x--3x-4 a. Why does f define a function? b. Find Dom fand Range f. c. Graph y = f(x) in detail. Include intercepts, symmetry, and asymptotes, including limit behavior for the asymptotes. d. Find the point where the graph crosses the horizontal asymptote.
Sketch the graph of two periods of the function. Label the key points showing intercepts, asymptotes, and the location of any maximum and minimum values. Give any phase shifts or vertical shifts as necessary. 6. Graph on the same axes f(x)= 3sin(x+1) Show 5 key points