Exponential Transformations from Graphs

Logarithmic functions are the inverse of...

• Linear Functions

• Exponential Functions 

• Quadratic Functions 

• Polynomial Functions 

What transformations have occurred on the graphs from the parent function to the transformed function? ** Use the grap given!!

• Reflection across the y-axis, shrink by a factor of 3, horizontal shift left 7 

• Reflection across the asymptote, horizontal shift right 3, vertical shift down 7 

• Reflection across the asymptote, stretch by a factor of 3, vertical shift down 7 

• Stretch by a factor of 3, vertical shift down 7 

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.

What is the domain and range of the function y=2^x ? Use the graph to help!

• Domain: (−∞,∞)

  Range: (0,∞)

• Domain: (−∞,∞)

  Range: (1,∞)

• Domain: (−2,∞)

  Range: (0,∞)

• Domain: (−∞,∞)

  Range: (−∞,0)

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

• 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,-∞)