Question

the black graph is y = f(x). choose the equation for the red graph. y/2 = f(x) 3y = f(x) y/3 = f(x) 2y = f(x)

Explanation:

Step1: Analyze vertical transformation

For a function $y = f(x)$, if we have $ay=f(x)$ (where $a
eq0$), it represents a vertical stretch or compression. When $x = 3$, for $y = f(x)$ the value is $y = 3$, and for the red - graph at $x = 3$ the value is $y = 1$.

Step2: Find the transformation factor

Let the equation of the red - graph be $ay=f(x)$. Substitute $x = 3$ into both $y = f(x)$ and $ay=f(x)$. We know $f(3)=3$ and $ay|_{x = 3}=1$. Substituting $f(3)$ into $ay=f(x)$ gives $a\times1 = 3$, so $a = 3$. The equation of the red - graph is $y/3=f(x)$.

Answer:

$y/3 = f(x)$