Parent Functions Transformations and End Behavior

• Reflection over x-axis

  Vertical shrink by 1/3

  Up 3

• Vertical shrink by 1/3

  Up 3

• Reflection over x-axis

  Vertical stretch by 2

  Up 3

• Vertical stretch by 2

  Up 3

• The end behavior of the graph is x →∞, f(x) →⁻∞ and x →⁻∞, f(x) →⁻∞

• The end behavior of the graph is x →∞, f(x) →∞ and x→⁻∞, f(x) →∞

• The end behavior of the graph is x →∞, f(x) →∞ and x→⁻∞, f(x) →2

• The end behavior of the graph is x →∞, f(x) →2 and x→⁻∞, f(x) →∞

Describe the transformations, asymptote, domain, and range for the following function: f(x)=-3(2)^(x-4)+6

• Transformation: Vertically stretched factor 3, translated right 4 and down 6. 
  Horizontal Asymptote at y = - 6 
  Domain: (-∞,∞)   Range: (-∞,6)

• Transformation: Reflection over x-axis, vertically stretched factor 3, translated right 4 and up 6. 
  Horizontal Asymptote at y = 6 
  Domain: (-∞,∞)   Range: (-∞,6)

• Transformation: Reflection over x-axis, vertically stretched factor 1/3, translated Left 4 and up 6. 
  Horizontal Asymptote at y = 6 
  Domain: (-∞,∞)   Range: (6,-∞)

• Transformation: Reflection over x-axis, vertically stretched factor 1/3, translated Left 4 and Down 6. 
  Horizontal Asymptote at y =6
  Domain: (-∞,∞)   Range: (6,-∞)

Describe how f(x) is transformed to describe g(x).

• The function f(x) would be translated left 1.

• The function f(x) would be translated right 1.

• The function f(x) would be translated down 1.

• The function f(x) would be translated up 1.

• A

• B

• C

• D

Describe the end behavior of
f(x) = 2x² + 6x⁵ + 10x

• Left side:  Rises
  Right side: Rises

• Left side: Falls
  Right side: Rises

• Left side:Rises
  Right side: Falls

• Left side: Falls
  Right side: Falls

Which of the following allows you to describe the end behavior of a polynomial?

• the degree and the constant

• the leading coefficient and the constant

• degree and the variable

• the degree and the leading coefficent

What are the transformations of this functions compared to the parent function?

• Shifted down 2

• Shifted up 2

• Shifted left 2

• Shifted right 2

What are the transformations of this functions compared to the parent function?

• Shifted right 5, shifted down 2, and reflected over the x-axis

• Reflected over the x-axis, vertical stretch, and shifted right 5

• Reflected over the x-axis, vertical stretch, and shifted left 5

• Shifted right 5, shifted down 2

What are the transformations to the graph compared to the parent function?

• Shifted right 2, shifted up 3, and reflected over the y-axis

• Shifted left 2, shifted up 3, and reflected over the y-axis

• Shifted left 2, shifted up 3, and reflected over the x-axis

• Shifted right 2, shifted up 3, and reflected over the x-axis