Given the rational functions, find the domain, state the roots and their multiplicities, x- intercepts, y-intercepts, equations of the vertical asymptotes, equation of a horizontal asymptote, sketch the graph of the rational function.

Q: -5 f(x) = x+5 %3D

A: Please see the answer below.

Q: Solve, a. Find the slant asymptote of the graph of the rational function f(x) =(x2 + x - 6)/(x - 3)…

A:

Q: Determine whether the graph of the rational function f(x) = x+6/x2+2x-24 has a vertical asymptote, a…

A: fx=x+6x2+2x-24      =x+6x2+6x-4x-24      =x+6xx+6-4x+6       =x+6x-4x+6 We notice that x+6…

Q: Find the intercepts and asymptotes, and then sketch a graph of the rational function and

A:

Q: Graph all vertical and horizontal asymptotes of the rational function. - 6 f(x)=2x-7 -5-

A:

Q: Solve,(a) state the domain of the function, (b) identify all intercepts, (c) find any asymptotes,…

A: Given: (a) state the domain of the function, (b) identify all intercepts, (c) find any asymptotes,…

Q: Find the vertical asymptotes, if any, the horizontal asymptote, if one exists, and the slant…

A: Given

Q: Solve, a. Find the slant asymptote of the graph of the rational function f(x) =(x2 - 1)/x. b. Follow…

A: Given, The function is                        a)

Q: Find the vertical asymptotes, if any, the horizontal asymptote, if one exists, and the slant…

A: We have given the rational function;

Q: Find the horizontal asymptote, if there is one, of the graph of the rational function: f(x) =…

A:

Q: Find the equation and sketch the graph of a rational function that passes through​ (0,0) and…

A: Given,         The graph of a rational function that passes through​ (0,0) and (5,10/9) ​, has the​…

Q: Find the slant asymptote, if any, of the graph of the rational function. x2 - 9x +9 20) f(x) %3D X+8

A:

Q: Find the horizontal asymptote, if there is one,of the graph of the rational function f(x) =12x/(3x2…

A: Concept: Given:

Q: Find the horizontal asymptote, if there is one, of the graph of the rational function: f(x) = (-3x +…

A:

Q: What are the vertical and horizontal asymptotes of the graph of y = 5-10x? Then graph the rational…

A: Vertical asymptote is the value for which the denominator is 0.

Q: Graph all vertical and horizontal asymptotes of the rational function. -5 f(x) = -3x-6

A: If degree of numerator is less than degree of denominator , the x-axis is the horizontal asymptote.…

Q: Find the domain of the rational function.

A:

Q: Find the slant asymptote, if any, of the graph of the rational function. 20) f(x) = x2-9x+9 x+8

A: For slant asymptotes of a rational expression where degree of numerator is greater than denominator…

Q: For each rational function, find (a) y-intercept point, (b) the roots, and (c) the equation of the…

A: Given function, fx=2x+3x-1

Q: Find the vertical asymptotes, if any, the horizontal asymptote, if one exists, and the slant…

A: The given function is g(x)=4x2-16x+162x-3 To find vertical asymptote, set the denominator equal to…

Q: domain

A:

Q: Graph the rational function. Show clearly all x- and y-intercepts and asymptotes, and state the…

A: To draw the graph of the function, rx=3x-12x+1 First, find out the x and y-intercept of the…

Q: Describe an asymptote, and explain when a rational function will have (a) a vertical asymptote and…

A: Asymptote

Q: Find the factors that are common in the numerator and the denominator. Then find the intercepts and…

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: Write an equation for a rational function with: Vertical asymptotes at x -3 and x -2 , %3D %3D…

A:

Q: Find the horizontal asymptote, if there is one, of the graph of the rational function: f(x) =…

A: Consider the rule, for finding the horizontal asymptote of any given rational function. For any…

Q: If you are given the equation of a rational function, explain how to find the vertical asymptotes,…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: 3- A. Give the equation of each vertical asymptote, and give the corresponding factor that will…

A: vertical asymptotefactor-2x+2-5x+5 The factor will appear in the denominator of the rational…

Q: Find the slant asymptote of the rational function. (Let y be the independent variable.) F(x) = 3x2…

A: A slant assymptote occurs when the numerator of the given function is of higher degree than…

Q: Find the common factors of the numerator and denominator of the rational function. Then find the…

A: r(x)=x2+5x-14x-2

Q: Solve, a. Find the slant asymptote of the graph of the rational function f(x) =(x3 + 1)/(x2 + 2x) b.…

A: fx=x3+1x2+2x a). x2+2x)x3+1(x-2           x3+2x2               -2x2+1               -2x2-4x…

Q: Find the horizontal asymptote, graph of the rational function. -7x+4 f(x)%3D 5x +2

A: We use leading coefficients for finding asymptote

Q: Graph all asymptotes of the rational function. 4x+ 2x-7 f (x) = 2x+ 3

A: f(x)=4x2+2x-72x+3vertical assymptotes:Denominator =02x+3=0⇒2x=-3x=-32Horizontal assymptotesNot…

Q: (3x-6)(x-4) x(r-4)

A: Domain of  3x-6x :  Solution:  x<0  or   x>0  Interval Notation: -∞ , 0∪0, ∞ Range of 3x-6x:…

Q: Graph all vertical and horizontal asymptotes of the rational function. -2 S(x) - 2x -7 3- 2+ -3+…

A: Given:- f(x) =-2/(-2x-7)  To find:- Graph of all vertical and Horizontal Asymptotes of given…

Q: Graph all vertical and horizontal asymptotes of the rational function. -2 f (x) = 3x+9 3- 2- -2- -3-…

A: Topic:- function

Q: Find the vertical asymptotes, if any, the horizontal asymptote, if one exists, and the slant…

A: Given rational function is fx=2xx2-9. To find vertical asymptote put denominator equal to 0.…

Q: Given the graph of a rational function, find the domain, state the roots and their multiplicities,…

A: The given question in which the image of graph is not clear.

Q: 1. A. Give the equation of each vertical asymptote, and give the corresponding factor that will…

A: Vertical Asymptotefactor-1x+1+1x-1 These factors ahould appear in the denominator of the rational…

Q: Write an equation for a rational function whose graph has all of the indicated features.

A: Write an equation for a rational function whose graph has all of the indicated features. -…

Q: Solve, a. Find the slant asymptote of the graph of the rational function f(x) =(x3 - 1)/(x2 - 9). b.…

A: Consider the provided rational function, fx=x3-1x2-9 Find the slant asymptote of the graph of the…

Q: If the graph of the rational function below appears to approach a vertical or horizontal line, then…

A: Graph of the rational functional is given, we have to find its equation.

Q: Find the factors that are common in the numerator and the denominator. Then find the intercepts and…

A: Given that  r(x) = x2+3x-10x+1x-3x+5 To factor of numerator x2+3x-10 = x2+5x-2x+10…

Q: Find the vertical asymptotes, if any, the horizontal asymptote, if one exists, and the slant…

A: Given: y=x2x+1 To find: The vertical asymptotes, if any the horizontal asymptote, if one exists and…

Q: Find the horizontal asymptote, if there is one,of the graph of the rational function f(x) =[15x/(3x2…

A: Given that: The rational function is f(x) = 15x3x2+1 .

Q: Give the equation of the vertical asymptote, and give the corresponding factor that will appear in…

A: At x = 2, we have the vertical asymptote has equation x = 2. The corresponding factor that will…

Q: State the vertical asymptote of the rational function. F(x)=(x-6)(x+6)/X^2-9

A:

Q: Solve, a. Find the slant asymptote of the graph of the rational function f(x) = (x2 - 4)/x. b.…

A: The given rational function is: fx=x2-4x a)- The slant asymptote of the graph is: The function can…