Question

the black graph is y = f(x). choose the equation for the red graph. y = f(x - 1) y/(-1) = f(x) y - 1 = f(x) y = f(x/(-1))

Explanation:

Step1: Analyze the transformation

The point $(3,3)$ on $y = f(x)$ is transformed to $(3, - 3)$ on the red - graph. The $x$ - coordinate remains the same and the $y$ - coordinate changes its sign. This indicates a reflection about the $x$ - axis.
The general rule for reflecting the graph of $y = f(x)$ about the $x$ - axis is $y=-f(x)$, which can be rewritten as $\frac{y}{-1}=f(x)$.

Answer:

$y/(-1)=f(x)$