Question

Instructions: Based on the information given in the problem, select the accurate transformation.

Answer 1

Given:

`\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}`

The graph of both functions is shown;

To know a stretch or compression, we use the rule below;

`\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}`

For the function f(6x),

`\begin{gathered} |b|=6 \\ Hence, \\ |b|>1 \\ \\ Thus\text{ it is a horizontal compression} \end{gathered}`

Therefore, the effect when function f(x) is replaced with f(6x) is a horizontal compression.