Question

the graph of y = f(x) is the solid black graph below. which function represents the dotted graph? answer y = f(x + 1) - 4 y = f(x - 1) - 4 y = f(x - 1) + 4 y = f(x + 1) + 4

Explanation:

Step1: Recall transformation rules

For a function $y = f(x)$, a horizontal shift $h$ units to the right is $y=f(x - h)$ and a vertical shift $k$ units up is $y=f(x)+k$.

Step2: Analyze horizontal shift

The dotted - graph is shifted 1 unit to the left of the solid graph. The rule for a left - shift of $h$ units for the function $y = f(x)$ is $y = f(x+h)$. Here $h = 1$, so there is a transformation of the form $y=f(x + 1)$.

Step3: Analyze vertical shift

The dotted - graph is shifted 4 units up from the solid graph. The rule for a vertical shift $k$ units up for the function $y = f(x)$ is $y=f(x)+k$. Here $k = 4$, so the transformation is $y=f(x)+4$.
Combining the horizontal and vertical shifts, the function of the dotted graph is $y=f(x + 1)+4$.

Answer:

$y = f(x + 1)+4$