Question

the graph of $y = f(x)$ is the solid black graph below. which function represents the dotted graph?
answer
$y = f(x+5)-4$
$y = f(x-5)-4$
$y = f(x-5)+4$
$y = f(x+5)+4$

Explanation:

Step1: Identify parent function points

Take a key point on $y=f(x)$, e.g., $(0,0)$ and $(-5,5)$.

Step2: Track dotted graph corresponding points

The matching point on the dotted graph for $(0,0)$ is $(-5,-4)$, and for $(-5,5)$ is $(-10,1)$.

Step3: Apply horizontal/vertical shift rules

For a point $(x,y)$ on $f(x)$, the transformed point is $(x-5, y-4)$. This matches the transformation $y = f(x+5) - 4$ (since $x' = x + 5 \implies x = x' -5$, substituting gives $y' = f(x') -4$).

Answer:

$y = f(x+5) - 4$