a. Find the slant asymptote of the graph of the rational function. b. Follow the seven-step strategy and use the slant asymptote to graph the rational function. x2 + 3x- 28 f(x) = X-7 What is/are the x-intercept(s)? Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The x-intercept(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers if needed.) B. There are no x-intercepts. Find the vertical asymptote(s). Select the correct choice below and, if necessary, fill in the answer box to complete the choice. A. The equation of the vertical asymptote is (Type an equation.) B. There is no vertical asymptote. u the horizontal asymptote(s). Select the correct choice below and, if necessary, fill in the answer box to complete the choice. O A. The uation of the horizontal asymptote is (Type an equation.) B. There is no horizontal asymptote. Plot points between and beyond the x-intercepts and the vertical asymptote. Evaluate the function at -9, -8, -2, 6, and 10. -8 - 2 6. 10 x² + 3x-28 flx)-

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

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

A: Explanation: Given that,  f(x)=-x(x-2)2   (a) Domain To find the domain of the function, we will set…

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

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

A: Solution:Givens(x)=2x-4x2+x-2

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Q: Graph the rational function. -6 f(x) = x-6 Start by drawing the vertical and horizontal asymptotes.…

A: Given,           The rational function is fx=-6x-6 .

Q: Find the horizontal asymptote, if there is one,of the graph of the rational function h(x) =12x3/(3x2…

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

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

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

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

A: f(t) = -t2+1t+5

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 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: Find the vertical and horizontal asymptotes, if any, of the rational function R(x) = 6x2 + x +…

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Q: BỊ Graph the given rational function by finding any symmetry, intercepts, asymptotes, and any…

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Q: BỊ Graph the given rational function by tinding any symmetry, intercepts, asymptotes, and any…

A: Given a function r(x)=2x2x2+4x-12 Let r(x)=y=2x2x2+4x-12 To find symmetry, intercepts, asymptotes of…

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

A: given,             rx=2x+6-6x+3

Q: Find the asymptotes and intercepts, construct the sign table and sketch the graph of the rational…

A: Given function is f(x)=x-32x+5 a) Vertical asymptotes are the values of x where function not…

Q: -x + 4x+3 2 f(x) = x-3

A: Given:      fx=-x2+4x+3x-3

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

A: The given function is h(x)=9x33x2+1   Known fact: If the degree (the largest exponent) of the…

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

A: Asymptotes of 4x2x2-2x-3 Vertical: x=-1, x=3, Horizontal: y=4   Axis interception points of…

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

A: Consider the given rational function rx=x3-3x2-10xx+2 Simplifying the function Taking x as common…

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Q: (a) Under what circumstances does a rational function have a slant asymptote? (b) How do you…

A: (a)  The form the rational function is P(x)Q(x) where, P(x) is the numerator and the Q(x) is the…

Q: Find the oblique asymptote of the rational function (-z-20) (z' +5z+6) f (z) = (z+4)(2z²-9z-5)

A: SOLUTION-

Q: Find the oblique asymptote of the rational function ( 2-z-20) (z+5z+6) f (1) = (z+4)(2z²-9r-5)

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

A: To find the x-intercepts, substitute t(x) with 0 in t(x)=x3-x2x3-3x-2 and factor x3-x2=0 to get…

Q: Find the vertical, horizontal, and oblique asymptotes, if any, for the given rational function 5x2 -…

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

A: Given that, the function is fx=3-2x-1. Note that, The degree of numerator is less than degree of…

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

A: Given function is s(x)=x+2(x+3)(x-1)=x+2x2+2x-3 Plugging x=0, we find y-intercept y=0+20+0-3  =-23…

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: 4b. Find the horizontal asymptotes, if any, of the graph of the rational function: 9x3 h(x) = 3x2 +…

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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: Find the x- and y-intercepts of the rational function. (If an answer does not exist, enter DI x² – 4…

A: To find the x and y-intercept of the below function. rx=x2−4x2

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

A: Given, rx=2x2+10x-12x2+x-6.   Find x-intercept by substituting x=0. r0=202+100-1202+0-6=2 Now,…

Q: Graph the rational function. 7 f (x) = X-2

A: For vertical asymptote we  set denominator =0  -x-2=0 x=-2   Since the degree of the numerator is…

Q: Graph the rational function. x+12x+10 f(x): 2x+4 Start by drawing the asymptotes. Then plot two…

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

A: Given rational function is fx=x3+27x+4. To find the x-intercept and y-intercept, asymptotes and draw…

Q: Graph the rational function f(x) = -4x -8 To graph the function, draw the horizontal and vertical…

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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: Find the x- and y-intercepts of the rational function.

A: Consider the rational function r(x)=x3+8x2+4 Recall that the x-intercepts occur at the points where…

Q: Graph the rational function. 2x2 7) f(x) =- x2 - 4 10 -10 -5 10 x

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

A: rx=4x-4x+2 To find x-intercepts, put rx=0, we get ⇒0=4x-4x+2⇒4x-4=0⇒x=1 Therefore x-intercept is 1,…

Q: Graph the rational function. f(x)=−4x^2−12x − 6/ 6x + 9   Start by drawing the asymptotes. Then…

A: We draw the graph of rational function.

Q: Graph the rational function. --7x f(x) = %3D x+x-20 Start by drawing the vertical and horizontal…

A: To draw: The vertical and horizontal asymptotes and also the intercepts of the function. Given…