Question

Given the parent logarithm function f(x)=log x, find the function g(x) after the parent function undergoes a vertical stretch by a factor of 3, and a horizontal shrink by a factor of 2.

Answer 1

Remember that:

• A function undergoes a vertical stretch if we ,multiply it all ,by a factor ,greater than 1

,

• A function undergoes a horizontal shrink if we ,multiply x, and only x, ,by a factor ,greater than 1

Thus,

`f(x)=\log (x)\rightarrow3\log (x)\rightarrow3\log (2x)`

Therefore,

`g(x)=3\log (2x)`