Solution:
Given:
[tex]\begin{gathered} Parent\text{ function: }f(x)=3^x \\ when\text{ f\lparen x\rparen is replaced with f\lparen6x\rparen} \\ The\text{ transformed function: }f(6x)=3^{6x} \end{gathered}[/tex]
The graph of both functions is shown;
To know a stretch or compression, we use the rule below;
[tex]\begin{gathered} For\text{ the function }f(bx) \\ when\text{ }|b|>1,\text{ it is a horizontal compression} \\ when\text{ }0<|b|<1,\text{ it is a horizontal stretch} \end{gathered}[/tex]
For the function f(6x),
[tex]\begin{gathered} |b|=6 \\ Hence, \\ |b|>1 \\ \\ Thus\text{ it is a horizontal compression} \end{gathered}[/tex]
Therefore, the effect when function f(x) is replaced with f(6x) is a horizontal compression.
