Transforming Rational Functions

Write a rational function with the given characteristics:
vertical asymptote at x = –3 and x = 5 a hole at x = 1

Describe how the graph of the function:f\left(x\right)=\frac{1}{x-2} can be obtainend by transforming the graph of the function:f\left(x\right)=\frac{1}{x}

• The graph of f is the graph of the reciprocal function shifted right 2 units and then stretched vertically by a factor of 1.
  

• The graph of f is the graph of the reciprocal function shifted left 1 unit and then stretched vertically by a factor of 2.

• The graph of f is the graph of the reciprocal function shifted right 1 unit and then stretched vertically by a factor of 2.

• The graph of f is the graph of the reciprocal function shifted left 2 units and then stretched vertically by a factor of 1.

• x = 1
  

• x = 0

• x = 7
  

• x = -4
  

• Translate up 2 units
  

• Reflect across the y-axis
  

• Reflect across the x-axis
  

• Vertically stretch by a factor of 6
  

• Translate left 1 unit
  

• There is a vertical asymptote and a slant (diagonal) asymptote
  

• There is a horizontal asymptote but no vertical asymptote
  

• There is no vertical asymptote
  

• There is a slant (diagonal) asymptote but no vertical asymptote
  

• There is a vertical and horizontal asymptote.
  

(Order matters) Select all possible combinations that correctly transforms:

y = g(x) to y = - 2g(x + 6) - 10

• Vert stretch by 2

  Reflect over horizontal axis

  Shifted down 10 units

  Shifted left 6 units

• Reflect over x-axis

  Vert stretch by 2

  Shifted left 6 units

  Shifted down 10 units

• Shifted down 10 units

  Shifted left 6 units

  Reflect over x-axis

  Vert stretch by 2

• Reflect over x-axis

  Vert stretch by 2

  Shifted down 10 units

  Shifted left 6 units

If the original graph is f(x) and the new graph has been moved 3 to the right, how would one write that in function notation?

• f(x - 3)

• f(x + 3)

• f(x) + 3

• f(x) - 3

Describe the order of transformations from the parent function g(x) =1/x, to f(x).

• horizontal translation by 2, vertical translation by 4

• reflection over the y-axis, horizontal translation by 2, vertical translation by 4

• reflection over the x-axis, horizontal translation by 2, vertical translation by 4

• horizontal translation by 2, vertical translation by 4, reflection over the x-axis