the graph of $y = f(x)$ is the solid black graph below. which function represents the dotted…

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

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

Answer

Explanation:

Step1: Identify parent function

The solid graph is $y = f(x) = |x|$, a V-shaped graph with vertex at $(0,0)$.

Step2: Analyze vertical reflection

The dotted graph is flipped over the x-axis, which corresponds to $y = -f(x) = -|x|$, with vertex at $(0,0)$.

Step3: Analyze horizontal shift

The dotted graph's vertex is at $(4, 0)$, which is a 4-unit shift right from $(0,0)$. A right shift by $h$ units transforms $y=-f(x)$ to $y=-f(x-h)$. Here $h=4$, so $y=-f(x-4)$.

Step4: Verify with a point

Take $x=0$ on dotted graph: $y=-f(0-4)=-|{-4}|=-4$, which matches the point $(0,-4)$ on the dotted graph. Take $x=4$: $y=-f(4-4)=-|0|=0$, which matches the vertex $(4,0)$.

Answer:

$y = -f(x - 4)$