Question

question 10 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

\\(\bigcirc\\) a. $f(x) = \frac{1}{3}(-x - 1)^5$

\\(\bigcirc\\) b. $f(x) = \left(-\frac{1}{3}x + 1\
ight)^5$

\\(\bigcirc\\) c. $f(x) = \frac{1}{3}(-x + 1)^5$

\\(\bigcirc\\) d. $f(x) = \frac{1}{3}(-x)^5 + 1$

Explanation:

Step1: Shift left 1 unit

Replace $x$ with $x+1$: $f_1(x)=(x+1)^5$

Step2: Vertically compress by $\frac{1}{3}$

Multiply by $\frac{1}{3}$: $f_2(x)=\frac{1}{3}(x+1)^5$

Step3: Reflect over y-axis

Replace $x$ with $-x$: $f_3(x)=\frac{1}{3}(-x+1)^5$

Answer:

C. $f(x)=\frac{1}{3}(-x+1)^5$