Question

what transformations have been applied to the function f(x) = -2(-x + 1)³? select all that apply. select all correct options vertical stretch by 2 x axis reflection horizontal compression by 1/2 y axis reflection

Explanation:

Step1: Rewrite the function

Rewrite $f(x) = -2(-x + 1)^3$ as $f(x) = -2(-(x - 1))^3 = -2(-1)^3(x - 1)^3 = 2(x - 1)^3$ is incorrect; instead, analyze transformations from parent function $g(x)=x^3$:
First, rewrite $f(x) = -2(-(x - 1))^3$.

Step2: Analyze vertical stretch

The coefficient $2$ outside the parenthesis means vertical stretch by 2.

Step3: Analyze x-axis reflection

The negative sign outside $2(-x+1)^3$ (i.e., $-2$) reflects over x-axis.

Step4: Analyze y-axis reflection

The $-x$ inside the parenthesis reflects over y-axis.

Step5: Analyze horizontal shift (not listed)

The $+1$ inside $(-x+1)$ is $-(x-1)$, so right shift 1, which is not an option. Horizontal compression is not present as there is no coefficient on $x$ other than $-1$ (which is reflection, not compression).

Answer:

• Vertical stretch by 2
• X axis reflection
• Y axis reflection