Describe three characteristics of the function y=log4x that remain unchanged under the following transformations

Question

Describe three characteristics of the function y=log₄x that remain unchanged under the following transformations: a vertical stretch by a factor of 3 and a horizontal compression by a factor of 2

Answer 1

It is not clear what your teacher is after.  However, here are some possibilities.

 

The original function is

 

y=log₄x

 

The transformed function is

 

y=(1/3)log₄(2x)

 

For both functions:

 

Domain is (0,∞)

 

Range is (-∞,∞)

 

They are continuous

 

They are both base 4 log functions.

 

They have continuous first derivatives.