Question

the graph of y = f(x) is the solid black graph below. which function represents the dotted graph? answer y = -f(x + 3) y = -f(x) + 3 y = -f(x) - 3 y = -f(x - 3)

Explanation:

Step1: Analyze vertical transformation

The dotted - graph is a reflection of the solid - graph about the x - axis. When \(y = f(x)\) is reflected about the x - axis, the transformation is \(y=-f(x)\).

Step2: Analyze horizontal transformation

The dotted - graph is also shifted downwards by 3 units. For a vertical shift downwards of \(k\) units for the function \(y = g(x)\), the new function is \(y = g(x)-k\). Since \(g(x)=-f(x)\) and \(k = 3\), the function of the dotted graph is \(y=-f(x)-3\).

Answer:

\(y=-f(x)-3\)