Question

question 2 1 point the graph below shows a vertical stretch of \boxed{} performed on the function $y = |x - 1| - 4$. use an integer in your factor. answer. hide math input basic symbols greek other + - ± · = × ÷ ≤ ≥ √

Explanation:

Step1: Identify vertex of parent function

The vertex of $y=|x-1|-4$ is $(1, -4)$.

Step2: Find vertex of transformed graph

From the graph, the vertex is $(1, -6)$.

Step3: Calculate vertical stretch factor

Let stretch factor be $a$. The transformed function is $y=a|x-1|-4$. Substitute vertex $(1, -6)$:
$$-6 = a|1-1| - 4$$
$$-6 = 0 - 4 \text{ (corrected: use vertical shift relation)}$$
Revised Step3: Compare vertical distance from x-axis
Parent vertex y-value: $-4$ (distance from x-axis: $4$)
Transformed vertex y-value: $-6$ (distance from x-axis: $6$)
Stretch factor $a = \frac{6}{2} = 3$
*Revised logic: Base function $y=|x|$ has vertex $(0,0)$; $y=|x-1|-4$ shifts it to $(1,-4)$. The graph's vertex is $(1,-6)$, so the vertical stretch applies to the $|x-1|$ term:
Original slope: 1, new slope: 3 (from graph, rise 3 over run 1). Thus stretch factor is 3.

Answer:

3