Transformations and Graphing

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.

This is an example of....

• an increasing exponential function

• a decreasing exponential function

• an increasing linear function

• none of the above

This is an example of.....

• exponential decay

• exponential growth

• constant change

• a linear function

• 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,-∞)

A parabola has a vertex at (-3,2).

What is the axis of symmetry?

• y = -2

• x = 3

• x = -3

• y = 2

Describe the transformation that occurred

p(x) = f(x + 3)

• Right 3 units

• Vertical Stretch

• Up 3 units

• Left 3 units

Describe the transformation that occurred.

h(x) = f(x) + 2

• up 2 units

• left 2 units

• Vertical Stretch

• right 2 units

Describe the transformations of f(x) when compared to the parent function. f(x)=(x+7)²

• horizontal shift left 7 units

• horizontal shift right 7 units

• vertical shift up 7 units

• vertical shift down 7 units