5. For each of the rational functions below: 2.0 + 1 x² +1 (a) f(x) =...
5. For each of the rational functions below: 2x + 1 (a) f(x) = x2 (b) g(x) = 2 find 2 + 1 3.12 (c) h(x) = T .x2 - 3.x + 2 (i) the domain of the function (use intervals to give your answers); (ii) all vertical asymptote(s) (if any); (iii) all horizontal asymptote(s) (if any); (iv) all r-intercept(s) (if any); (v) all y-intercept(s) (if any). Write yotir answers in the following table: ydir polynomial domain Vertical Asymptote Horizontal...
12 (Rational Functions) For each rational function below, find (a) the vertical asymptote(s). (b) the horizontal asymptote. (c) the x-intercept(s). (d) the y-intercept. (e) the graph of the function. 2x-6 (1) y X-2 x-5 (2) y 1+ x2-1 12 (Rational Functions) For each rational function below, find (a) the vertical asymptote(s). (b) the horizontal asymptote. (c) the x-intercept(s). (d) the y-intercept. (e) the graph of the function. 2x-6 (1) y X-2 x-5 (2) y 1+ x2-1
1. Given, the rational function below, sketch a neat and labeled graph by filling in each of the blanks with appropriate work: 2x² + 8x f(x)= x-2 a) Domain in intervals b) Equation of vertical asymptote(s), if any c) Equation of horizontal asymptote or slant asymptote, if any (write n and m). d) Ordered pair(s) of point where function touches its horizontal or slant asymptote c) x-intercept(s) and its y-intercept, if any Test for symmetry and state your conclusion
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)...
00 The information below tells us about the behavior of the rational function f around its asymptotes. Use this information to answer the following questions. limf(1) = 5 f(3) =5 lim S(z) = 00 $(x) = -00 lim f(3) = 0 lim f(x) = 0 • The only horizontal intercept: (- 1.8,0). a. What is the vertical asymptote(s) of the functions. If there is no vertical asymptote, write DNE. Separate multiple answers with a comma lim -5 Preview b. What...
Graph by analyzing the given rational function: R(x) = -1 Domain: Rin lowest terms: x-intercept(s) and its multiplicity (cross or touch): y-intercept(s): Vertical asymptote(s), if any. Determine the behavior of the graph of R on either side of each vertical asymptote. Horizontal asymptote or oblique asymptote, if any: Additional points
Please tell me which options I need to select and what I have to type in. Thank you! 3-3x For the given rational function f(x)- x- find the following (A) Find the intercepts for the graph. (B) Determine the domain. (C) Find any vertical or horizontal asymptotes for the graph (D) Sketch any asymptotes as dashed lines. Then sketch a graph of y f(x) (A) Identify the x-intercepts, if there are any. Select the correct choice below and, if necessary,...
The graph of a rational function fis 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) Find all x-intercepts and y-intercepts. Check all that apply. X-intercept(s): 4 00 01 None . : O=D y-intercept(s): 01 04 00 None Dando None (0,0) HHH [0,0] (0,0] [0,0) (b) Write the equations for all vertical and horizontal asymptotes. Enter the equations using the "and" button as necessary....
Learning Goal: Be able to sketch the curves of rational functions. 1. Sketch the following function by stating: i) The x-intercepts and y-intercepts ii) The equation(s) of the Vertical Asymptote and the function's End Behaviours near it. iii) The equation of the Horizontal Asymptote and the function's End Behaviours near it. f(x) = 4x + x2 x' – 4x - 12
2. Let f(x) = x2+3x-10 x2+x-6 (a) Find the y-intercept. Show all work. (b) Find the x-intercept. Show all work. (c) Find the vertical asymptote(s). Show all work. (d) Find the horizontal asymptote. Explain your solution. (e) Does the rational expression have any holes? Explain.