Question 5 of 10
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. $f(x)=\left(-\frac{1}{3} x+1\right)^{5}$
B. $f(x)=\frac{1}{3}(-x)^{5}+1$
C. $f(x)=\frac{1}{3}(-x-1)^{5}$
D. $f(x)=\frac{1}{3}(-x+1)^{5}$
Answer
\(\boxed{\text{The correct answer is D. } f(x)=\frac{1}{3}(-x+1)^{5}}\)
Step 1 ：The original function is \(f(x)=x^{5}\).
Step 2 ：A shift to the left by 1 unit would result in the function \(f(x)=(x+1)^{5}\).
Step 3 ：A vertical compression by \(\frac{1}{3}\) would result in the function \(f(x)=\frac{1}{3}(x+1)^{5}\).
Step 4 ：A reflection over the y-axis would result in the function \(f(x)=\frac{1}{3}(-x+1)^{5}\).
Step 5 ：\(\boxed{\text{The correct answer is D. } f(x)=\frac{1}{3}(-x+1)^{5}}\)
