Question

transform the solid black function to match the dotted function. ( y = x^2 ) ( f(x)=\boxed{0}+\boxed{0}f(x) )

Explanation:

Step1: Identify base function

The solid black function is $f(x) = x^2$.

Step2: Analyze direction of reflection

The dotted function is a vertical reflection of $f(x)$ across the x-axis, which uses the transformation $-f(x)$.

Step3: Confirm no shift needed

The vertex of both functions is at $(0,0)$, so no horizontal/vertical shift (the blanks for $h$ and $k$ in $-f(x+h)+k$ are 0).

Answer:

$-f(x+0)+0$ or simplified as $-x^2$