Answer:
f(x) is shrinked
Explanation:
Given
![f(x) = 4^x](https://img.qammunity.org/2022/formulas/mathematics/high-school/djf67c1fru4rjpwaox0j3257ivcwj9tttr.png)
![g\left(x\right)=(1)/(3)\cdot4^x](https://img.qammunity.org/2022/formulas/mathematics/high-school/pxztxlkba6yycsvxyky72jt9lgbfubohbi.png)
Required
The effect of dilation on f(x)
From the given parameters, we have:
![f(x) = 4^x](https://img.qammunity.org/2022/formulas/mathematics/high-school/djf67c1fru4rjpwaox0j3257ivcwj9tttr.png)
![g\left(x\right)=(1)/(3)\cdot4^x](https://img.qammunity.org/2022/formulas/mathematics/high-school/pxztxlkba6yycsvxyky72jt9lgbfubohbi.png)
On a general term;
![g(x) = k * f(x)](https://img.qammunity.org/2022/formulas/mathematics/high-school/5fuvec9hwzigsderewexou60cx8ma5tk77.png)
So by comparison:
![k = (1)/(3)](https://img.qammunity.org/2022/formulas/mathematics/high-school/meg0xyo2c5bppeo86nalgq2kbnf9jr9q3z.png)
When scale of dilation is less than 1, it means the function is reduced. Hence, the specific effect on f(x) is shrink