Which function results after applying the sequence of transformations to $f(x)=x^{5} ?$
- shift left 1 unit
- vertically compress by $\frac{1}{3}$
- reflect over the $y$-axis
A. $f(x)=\frac{1}{3}(-x)^{5}+1$
B. $f(x)=\frac{1}{3}(-x-1)^{5}$
C. $f(x)=\left(-\frac{1}{3} x+1\right)^{5}$
D. $f(x)=\frac{1}{3}(-x+1)^{5}$

Step 1 ：Given the function \(f(x)=x^{5}\), we are to apply a sequence of transformations in the order they are given.

Step 2 ：First, we shift the function 1 unit to the left. This transformation is equivalent to replacing \(x\) with \((x+1)\) in the function. So, \(f(x)=x^{5}\) becomes \(f(x)=(x+1)^{5}\).

Step 3 ：Next, we vertically compress the function by \(\frac{1}{3}\). This transformation is equivalent to multiplying the function by \(\frac{1}{3}\). So, \(f(x)=(x+1)^{5}\) becomes \(f(x)=\frac{1}{3}(x+1)^{5}\).

Step 4 ：Finally, we reflect the function over the y-axis. This transformation is equivalent to replacing \(x\) with \(-x\) in the function. So, \(f(x)=\frac{1}{3}(x+1)^{5}\) becomes \(f(x)=\frac{1}{3}(-x+1)^{5}\).

Step 5 ：Thus, the function that results after applying the sequence of transformations to \(f(x)=x^{5}\) is \(f(x)=\frac{1}{3}(-x+1)^{5}\).

Step 6 ：\(\boxed{\text{Final Answer: } f(x)=\frac{1}{3}(-x+1)^{5}}\)