By transforming the graph of y = log(base2)(x) , sketch the graph of f(x) = 2 - log(base2)(x - 1). What is the domain and range of f(x)?

Question

By transforming the graph of y = log₂(x) , sketch the graph of f(x) = 2 − log₂(x − 1).

What is the domain and range of f(x)?

Answer 1

Original function:

 

f(x) = log₂(x)

 

 

Transformed function:

 

f(x) = -log₂(x - 1) + 2

 

 

The transformation process is to take  f(x)=log₂(x)   and shift it to the right 1 unit and shift 2 units up.  Then flip it down.

 

A log cannot have a negative value for an argument.  Set the argument greater than zero.

 

x - 1 > 0

 

x > 1

 

 

The domain is all values greater than 1.

 

 

To find the range, use the domain.

 

Evaluate f(1.00001), f(2) , f(200), and f(2000)

 

Then use those values to determine the range.