Question

the following transformations were done to $f(x) = x^3$: up by 2 and flipped over the x - axis, not necessarily in that order.
what is the equation of the transformed function?
$f(x) = \square$
what is the transformed functions domain? write your answer in interval notation.
answer: $\square$
question help: \message instructor

Explanation:

Step1: Case 1: Shift first, then flip

Start with $f(x)=x^3$. Shift up by 2: $x^3 + 2$. Flip over x-axis: $-(x^3 + 2) = -x^3 - 2$.

Step2: Case 2: Flip first, then shift

Start with $f(x)=x^3$. Flip over x-axis: $-x^3$. Shift up by 2: $-x^3 + 2$.

Step3: Analyze domain of transformed functions

Cubic polynomials are defined for all real numbers.

Answer:

Equation of transformed function: $\boldsymbol{-x^3 - 2}$ or $\boldsymbol{-x^3 + 2}$
Domain: $\boldsymbol{(-\infty, \infty)}$