Graphs of Rational Functions

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Questions

• What are Rational Functions?
• Why do Rational functions have asymptotes?
• How do you graph rational functions?
• What are asymptotes?
• How do you find points of discontinuity in rational functions?
• How do you find the points of discontinuity and the asymptote for the function #y=6/(x-5)#?
• How do you identify the vertical and horizontal asymptotes for rational functions?
• How do you graph #y=\frac{x}{2-x^2}-3#?
• How do you find the x intercept of #f(x) = (x^2+9x)/(x^2+3x-4)#?
• How do you graph the rational function #f(x)=6/(x^2+x-2)#?
• How do I graph the function: #y=(2x)/(x^2-1)#?
• How do I graph the rational function: #y=-6/x+4#?
• How do you graph #y = 1/(x+2) - 1#?
• How do you graph #f (x) = (24x – 156) /( 36 – x^2)#?
• How do you graph #f(x) = -1 / (x+1)#?
• How do you graph #f(x)=x^2/(x+5)#?
• How do you graph #f(x) = (2x^2 + x - 3) / (2x^2 - 7x)#?
• How do you find the zeroes for #R( x) = (3x)/(x^2 - 2x)#?
• How do you graph #f(x)=x/(x+2)#?
• How do you graph #f(x)=(2x^2 + 5) / (x-1)#?
• How do you graph #y = 3/x #?
• How do you graph #y =1/(x+3)#?
• How do you graph #y=1/(x^2-x-6)#?
• How do you graph #(x^2+3x-4)/x#?
• How do you graph # (x)/(x^2-4)#?
• How do you graph #f(x) = (4x^2-36x) / (x-9)#?
• How do you graph #f(x)= (x^2 +10x+ 24)/( x+6)#?
• How do you graph #f(x)= (x^2-100)/(x+10)#?
• How do you graph # f(x)= (2x^2+5x-12)/(x+4)#?
• How do you graph # f(x)= (3x^2-7x-6)/(x-3)#?
• How do you graph #f(x)=(x-2) / (x+2)#?
• How do you graph #y= x/(x-4)#?
• How do you graph #R(x) = (x + 2)/(x^2 - 4)#?
• How do you graph # f(x)= x/(x+3)#?
• How do you graph #(3x + 3) / (2x + 4)#?
• How do you graph #(2x)/(x-4)#?
• How do you graph #(-5x)/(x+3)#?
• How do you graph #F(x)=((4x^2)+8x-32)/((2x^2)-6x+4)#?
• How do you graph #(x^2-4)/(x^2-9)#?
• How do you graph #(x^3-6x+5)/(x^2-3)#?
• How do you graph #f(x)= (x^3+1)/(x^2-4)#?
• How do you graph #f(x)=(x+2)(x-1)/(x-3)#?
• How do you graph #(2x^2) /( x^2 - 9)#?
• How do you graph #f(x)=1/x -4#?
• How do you graph #y=1/[x(x-2)]#?
• How do you graph #(6x^2 + 10x - 3) /( 2x + 2)#?
• How do you graph #y= (2x)/(x-1)#?
• How do you graph # f(x) =(x)/(x^2-4)#?
• How do you graph #y=(x-1)/(x-2)#?
• How do you graph #y = (7x)/x^2#?
• How do you graph #y =(2x(x-2)) / ((x-3) (x+1))#?
• How do you graph #y =(x^(1/2) +1)/(x+1)#?
• How do you graph #y =(8x-4x^2)/((x+2)^2)#?
• How do you graph #y =(2x + 1)/(x-5)#?
• How do you graph #y =7/x#?
• How do you graph #y =(x^2+4x-2)/(x^2-x-7)#?
• How do you graph #y =1/x^2#?
• How do you graph #y =1/(x-4)#?
• How do you graph #y =(x^2-3)/(x-1)#?
• How do you graph and find the discontinuities of #y=2/(x+1)#?
• How do you graph and find the discontinuities of #y=(3x) /( 4-x^2)#?
• How do you graph and find the discontinuities of #y=(-4x-3)/(x-2)#?
• How do you graph and find the discontinuities of # y = 3/x#?
• How do you graph and find the discontinuities of #f(x) = 1/x #?
• How do you graph and find the discontinuities of #(x^(1/2) +1)/(x+1) #?
• How do you graph and find the discontinuities of #F(x) = (-2x^2 + 1)/(2x^3 + 4x^2)#?
• How do you graph and find the discontinuities of #R(x) = (x^2 + x - 12)/(x^2 - 4)#?
• How do you graph and find the discontinuities of #H(x) = [(x - 1) (x + 2) (x - 3)]/(x(x - 4)^2#?
• How do you graph and find the discontinuities of #(x^2-25)/(x^2+5x)#?
• How do you graph and find the discontinuities of #(x^2)/(x-1)#?
• How do you graph and find the discontinuities of #(x^2-1)/(x^2+4)#?
• How do you graph and find the discontinuities of #f(x) = (x - 1) / (x^2 - x - 6)#?
• How do you graph and find the discontinuities of #f(x)=1/x^2#?
• How do you graph and find the discontinuities of #f(x)=1/x -4#?
• How do you graph and find the discontinuities of #1 /(x+6)#?
• What are the important parts of the equation to graph #f(x) = (x^2 - 1) / (x+1)#?
• Which quadrant does # y=x/(x^2+2x+1)# lie?
• How do you graph #g(x) = (x-4)^2/(x+2)#?
• How do you graph #y = 3/x #?
• How do you find the asymptotes of # (1) / (x-1) ^ 2#?
• What is a rational function that has x=4 and x=3 as vertical Asymptotes, and (-2,0) as an x-intercept?
• Question #ed439
• How do you graph # f(x)=1/x#?
• How do you graph #f(x) = x + (5x)/(x-1)# and identify all the asymptotes?
• How do you graph #f(x)= (2x^2+7x-15) / (x+5)# and identify all the asymptotes and domain?
• Given #f(x)= (2x-1)/(x-1)#, what is the y intercept, and x intercept?
• How do you create a rational function that includes the following: crosses x-axis at 4, Touches the x-axis at -3, One vertical asymptote at x=1 and another at x=6, one horizontal asymptote at y= -3?
• How do you write an equation for a rational function that has a vertical asymptote at x=2 and x=3, a horizontal asymptote at y=0, and a y-intercept at (0,1)?
• How do you write a rational function that has the following properties: a zero at x= 4, a hole at x= 7, a vertical asymptote at x= -3, a horizontal asymptote at y= 2/5?
• What is a rational function that satisfies the following properties: a horizontal asymptote at y=3 and a vertical asymptote of x=-5?
• How do you determine the asymptotes of #y = (3x)/(x + 4)#?
• Question #13eae
• How do you graph #f(x)=(x-2)/(x-4)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x+4)/(-2x-6)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x^2-12x)/(x^2-2x-3)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(2x^2+10x+12)/(x^2+3x+2)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=3/(x-2)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=4/(x-1)+1# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=-3/(x-1)-1# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=-3/x# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=3/(x+1)-2# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=3/x+1# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=2/(x-3)+1# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x^2-5x+6)/(x^2-4x+3)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x-4)/(x^2-3x)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x^2+3x)/(x^2-x)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(-3x^2-12x-9)/(x^2+5x+4)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x^3-16x)/(-3x^2+3x+18)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x^2+x)/(-2x^2-2x+12)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(2x^3-2x^2)/(x^3-9x)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(-x-1)/(x+2)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x^2+4x+3)/(-3x-6)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x^3-x)/(x^3+2x^2-3x)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x^2+3x)/(-4x+4)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x^2+3x+2)/(-3x-12)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x^3-2x^2-3x)/(4x^2+8x)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x-3)/(-2x-8)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x^2+7x+12)/(-4x^2-8x+12)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x-1)/(x+1)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=x/(x-2)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=x/(x^2-1)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(2x^2)/(x^2-9)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x^2-4)/(x^2+4)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x+3)/((x+1)(x-3))# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x^2-2x)/(x^2-4)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x^2-16)/(x^2-6x+8)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x^2-x-2)/(x^2-2x+1)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(1-x^2)/x# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(2x)/(3x-1)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=3/(x^2(x+5))# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=2/(x-1)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=8/(x(x+2))# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=x/(x^2-9)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=2/(x-1)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=x^2/(x-4)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(4(x+1))/(x(x-4))# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x^2-2x-8)/(x^2-9)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(2x^3+x^2-8x-4)/(x^2-3x+2)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(2x^2-5x+2)/(2x^2-x-6)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=2/(x-1)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=-2/(x+3)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x^2-1)/x# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x+12)/(x^2-x-6)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=7/(x+4)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=1/(x^2-16)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(3x+8)/(x-2)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(2x^2)/(x-3)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(3x^2+2)/(x+1)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=-2/x# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=-1/(x-2)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=x/(x-2)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=1/(x^2-2x)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=-(x+4)/2# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x^2+2x+1)/x# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=-3/(x-1)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=-2/(x^2+x-2)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(2x-1)/(x+3)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(5-2x)/(x-2)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=1/x^2# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=2/(x^2-4x+4)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(2x-3)/(x^2+x-6)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(3x^2-2x)/(x-1)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=x/(x^2+x-2)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(x-1)/x^2# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=2/(x^2+1)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(2x-1)/(x^3-9x)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=(2x^2+1)/(x^3-x)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=x^2/(x+1)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• How do you graph #f(x)=x^2/(x-1)# using holes, vertical and horizontal asymptotes, x and y intercepts?
• What are the asymptotes for #y=2/x# and how do you graph the function?
• What are the asymptotes for #y=-4/(x+2)# and how do you graph the function?
• What are the asymptotes for #y=3/(x-1)+2# and how do you graph the function?
• What are the asymptotes for #y=2/(x+1)-5# and how do you graph the function?
• What are the asymptotes of #y=5/x# and how do you graph the function?
• What are the asymptotes of #y=-3/x# and how do you graph the function?
• What are the asymptotes of #y=2/x+3# and how do you graph the function?
• What are the asymptotes of #y=1/x-2# and how do you graph the function?
• What are the asymptotes of #y=1/(x+3)# and how do you graph the function?
• What are the asymptotes of #y=1/(x-2)# and how do you graph the function?
• What are the asymptotes of #y=-2/(x+1)# and how do you graph the function?
• What are the asymptotes of #y=4/(x-1)# and how do you graph the function?
• What are the asymptotes of #y=1/(x-2)+1# and how do you graph the function?
• What are the asymptotes of #y=3//(x-1)-2# and how do you graph the function?
• What are the asymptotes of #y=2/(x+1)-4# and how do you graph the function?
• What are the asymptotes of #y=-1/(x+4)+3# and how do you graph the function?
• What are the asymptotes of #y=x^2/(x^2-1)# and how do you graph the function?
• What are the asymptotes of #y=x/(x^2-9)# and how do you graph the function?
• Without graphing, what is the transformation that takes place between the graph #y=1/x# and the graph of #y=1/(x+5)-2#?
• How do you write a rational function if the asymptotes of the graph are at #x=3# and #y=1#?
• What are the excluded values for the rational expression #8/(x^2-16)#?
• What are the excluded values for the rational expression #(3m)/(m^2-6m+5)#?
• How do you find the zeros for the function #f(x)=(x^2-x-12)/(x-2)#?
• How do you find the zeros of the function #f(x)=(x^2-x-12)/(x^2+2x-35)#?
• How do you find the zeros of the function #f(x)=(x^2+3x-4)/(x^2+9x+20)#?
• How do you find the zeros of the function #f(x)=(20x^2+11x-40)/(2x+5)#?
• How do you find the zeros of the function #f(x)=(3x^2-18x+24)/(x-6)#?
• How do you find the zeros of the function #f(x)=(x^3+x^2-6x)/(x-1)#?
• How do you find the zeros of the function #f(x)=(x^3-4x^2-12x)/(x+2)#?
• How do you simplify #(3a^2b^4+9a^3b-6a^5b)/(3a^2b)# and what are the ecluded values of the variables?
• How do you simplify #(8x^5-10xy^2)/(2xy^2)# and what are the excluded values of the variables?
• How do you simplify #(x+5)/(3x^2+14x-5)# and what are the excluded values of the variables?
• How do you compare and contrast the graphs of #y=x-2# and #y=(x^2+5x-14)/(x+7)#?
• Explain why every polynomial is also a rational expression?
• How do you find the asymptote and graph #y=2/x#?
• How do you find the asymptote and graph #y=1/(x-5)-4#?
• How do you find the asymptote and graph #y=1/(x+3)#?
• How do you find the asymptote and graph #y=-1/(x+6)+7#?
• How do you find the zeros of #f(x)=(x+2)/(x^2-6x+8)#?
• How do you find the zeros of #f(x)=(x^2-3x-4)/(x^2-x-12)#?
• How do you find the zeros of #f(x)=(x^2+6x+9)/(x^2-9)#?
• Question #5e2ab
• Question #5e8db