Where (for what values of x) does the rational function (x – 3)(x + 4) - f(x) = 36 (x + 74)(x – 3)(x – 79) - have (a) holes? (b) vertical asymptotes?

Q: Write an equation for a rational function with: Vertical asymptotes at x = – 4 and x = 2.…

A: Given: Vertical asymptotes are at x=-4 and x=2. x-intercepts at -1,0 and 5,0. y-intercept at 0,1…

Q: The graph below belongs to a rational function f(z) = p(z) with horizontal and vertical asymptotes y…

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Q: Graph all vertical and horizontal asymptotes of the rational function. 2x+5 S(x) = 2x-1

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Q: Find a rational function that satisfies the given conditions. Which rational function satisfies the…

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Q: Find the limit of the rational function (a) as x→∞ and (b) as x→ - o. 2x° + 3x2 - 1 f(x) = 9x° - 5x+…

A: a).  Given: limx→∞ 2x9+3x2-19x5-5x+9 Now find the limit. limx→∞ 2x9+3x2-19x5-5x+9=limx→∞…

Q: x³ - 2x? + 4x - 8 x² - 11x + 18 is undefined. Determine whether an asymptote or a hole Determine…

A: We have given function Rx=x3-2x2+4x-8x2-11x+18 Function is undefined where denominator is zero. If,…

Q: What is the equation for the horizontal asymptote of the rational functional graph? 1) y=2 2)Y=3…

A: The domain of the given function is, D=x|x≠2 The rage of the function is,

Q: Determine a rational function that meets the given conditions, and sketch its graph. The function f…

A: For vertical asymptotes of a rational function, take denominator zero

Q: 11. Sketch the rational function: f(x) "Hole" Sketch Domain Range VA HA Label graph = x2-5x+4…

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Q: The graph of a rational function has vertical asymptotes at x=- and r=1, x-intercepts at 2 (-4, 0)…

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Q: ах + b Write a rational function in the form of f(x)= that has a zero at x=-1, a vertical asymptote…

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Q: Find the vertical, and horizontal asymptote of rational function. Vertical Asymptote Horizontal…

A: Vertical and horizontal asymptote

Q: 5æ? and For the rational function f(x) there are vertical asymptotes at x = x2 - 5x +6 a horizontal…

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Q: 16. Construct an equation of a rational function whose graph has a hole at the coordinates (-2, 0),…

A: Given, x=1, x=-3, y=-5 are vertical and horizonatal asymptote. vertical asymtote is the denominator…

Q: 4. Let (x) - 6x² + 13x+7 3x + 2 What is the equation of the oblique asymptote of f(x)? From what…

A: Solution

Q: 6. Sketch the rational function: f(x) = = "Hole" Sketch -6 Domain Range VA HA . Label graph -2 of:…

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Q: Write a formula for a rational function with the following properties: a removable singularity…

A: Rational function.

Q: Graph the rational function. 2x-3 f(x) = ーx+3 Start by drawing the vertical and horizontal…

A: Solution

Q: x-1 f (x) = -2 y=0 y=1 y=1/2 No horizontal asymptote

A: If the degree of the denominator is bigger than the degree of the numerator, the horizontal…

Q: The following question is about the rational function (x + 1)(x – 2) (x + 2)(x – 4) r(x) The…

A: We get the vertical asymptotes when the denominator of the function is zero.

Q: 1. Write an equation of a rational function that satisfies ALL of the given the given conditions…

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Q: 2) Give an example of an equation of a rational function Q satisfying all of the conditions:…

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Q: Find an equation of a rational function f that satisfies the given conditions. vertical asymptotes:…

A: Solution:-Given ,vertical asymptotes:x=-5,x=3horizontal asymptote:y=0x-intercept:-1;f(0)=-2hole at…

Q: The following question is about the rational function r(x) =  (x + 1)(x − 2) (x + 2)(x − 9)…

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Q: Where (for what values of x) does the rational function (x + 28)(x – 92) f(x) 12 x + 97)(x + 16)(x +…

A: Let f(x)=p(x)q(x) be a rational function then if p and q have a common factor (x-a) that…

Q: ах + b State the equation of a rational function in the form of f(x)= if the vertical asymptote is…

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Q: Find the vertical, and horizontal asymptote of rational function. Vertical Asymptote Horizontal…

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Q: Graph the rational function. 2 f(x)= x+1 Start by drawing the vertical and horizontal asymptotes.…

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Q: 14. How do you find the horizontal asymptote of a 4x²+x-1 rational function f(x) = in terms of…

A: Horizontal Asymptotes :- A function f(x) will have the horizontal asymptote y=L  if either…

Q: 8. Graph the rational function. horizontal asymptotes. 3x-12 a. r(x)= x+1 Show clearly all x- and…

A: Graphs are to be drawn first and then asymptotes and intercepts need to be marked.

Q: 3–6 ■ The following questions are about the rational function

A: Given rational function is: rx=x+1x-2x+2x-3 (3) The function r has x-intercepts where:…

Q: Determine the equation of a rational function f (x) = 8х — 4 that has a vertical asymptote at x = -…

A: Given query is to find the the function with given horizontal and vertical asymptot. Aa

Q: Create a rational function that matches everything below Has zero at (3,0) has a hole at (-1,4)…

A: Here is the solution of the given problem

Q: 6. The rational function f(x) = + k is transformed to g(x) = -5f(x+3)-1. Which row in the table x-2…

A: Given that fx=1x-2+k is transformed to gx=-5fx+3-1. The objective is find the asymptotes that best…

Q: Give a rational function with the following characteristics:  a horizontal asymptote of 3, vertical…

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Q: 32. The rational function y 7x has a horizontal asymptote at y =a and a vertical x -2 asymptote at æ…

A: The given rational function is y=7xx-2

Q: Find an equation of a rational function f that satisfies the given conditions. vertical asymptotes:…

A: Vertical asymptotes at x=-2 and x=3 means (x+2) and (x-3) are denominator factors. Horizontal…

Q: 1. f(x) x + 4 2x² –13x -7 ||

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Q: If the rational function  y = r(x)  has the vertical asymptote  x = 3,  then as  x → 3+,  either  y…

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Q: symptote of the rational function y = ax2 +bx+c/x-2 passes through the origin,(0,0). PROVE that…

A: In the given question, the concept of slant asymptote is applied. Slant Asymptote Because the degree…

Q: Write a rational function that meets the following criteria: Vertical asymptote at x=1 Horizontal…

A: Function has vertical asymptotes , horizontal asymptotes and has a hole. At asymptotes function is…

Q: -2(x+1)(x+4) (x+2)°(x-3) -(x+1)(x+4)² 2(x-2) (x+3) -2(x-1)(x-4) (x-2)° (x+3) A) R(x) =: B) R(x) =:…

A: We have to find the function using the given data

Q: The horizontal asymptote of f(x)=0.8^x is y=0 what is the horizontal asymptote of h(x)=0.8^x-10

A: Given   h(x)=0.8x-10Horizontal Asymptoteline y=L is a horizontal asymptote of the functiony=f(x), if…

Q: The following question is about the rational function (x + 1)(x - 3) (x + 3)(x - 7) r(x) = The…

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Q: 2=2–5z+1, What are the asymptotes of the rational function y T-2 Vertical Asymptote: Horizontal…

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Q: 9. State the equation of a rational function that has all of the following: Holes at x -5, x 1…

A: NOTE: Refresh your page if you can't see any equations. . here vertical asymptote is x=3 so the…

Q: 2x-x2 x2 – 4x+3 Describe the behavior of the rational function y= near vertical asymptote x = 1.…

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Q: che equation for the horizontal asymptote of the rational function grap

A: Given,

Q: 1. For the rational function g(x)= x'+7x+12 r+x-6 (a) Explain why x=2 is a vertical asymptote. (b)…

A: Explanation of the answer is as follows