Learning Goal: Be able to sketch the curves of rational functions. 1. Sketch the following function...
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
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...
5. For each of the rational functions below: 2.0 + 1 x² +1 (a) f(x) = (b) g(x) = . 2 2 find (c) h(x) = 3.2 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 z-intercept(s) (if any); (v) all y-intercept(s) (if any). Write your answers in the following table: polynomial domain Vertical Asymptote Horizontal Asymptote x-intercept...
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
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.
Write an equation for a rational function with: Vertical asymptotes at x = -3 and x = 5 x intercepts at x = -1 and x = 4 Horizontal asymptote at y=9 y = Preview
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,...
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...
12 Find the equation and sketch the graph of a rational function that passes through (0,0) and 6,35 . has the x-axis as a horizontal asymptote, and has two vertical asymptotes x- 1 and x1 The equation of the function is y (Simplify your answer. Use integers or fractions for any numbers in the equation.) Choose the correct graph below. в. Ос. O D.
O POLYNOMIAL AND RATIONAL FUNCTIONS Writing the equation of a rational function given its graph 3 . The figure below shows the graph of a rational functionſ. It has vertical asymptotes x -1 and x=6, and horizontal asymptote y The graph has x-intercept 4, and it passes through the point (2, -1). The equation for f(x) has one of the five forms shown below. Choose the appropriate form for f (x), and then write the equation. You can assume that...