Question

question 2 the graph below shows a vertical stretch of factor performed on the function ( y = |x - 1| - 4 ). use an integer in your answer.

Explanation:

Step1: Identify vertex of parent function

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

Step2: Find vertex of transformed graph

From the graph, the vertex is at $(1, -12)$.

Step3: Calculate vertical stretch factor

Let stretch factor be $k$. The transformed function is $y=k|x-1|-4$. Substitute vertex $(1,-12)$:
$-12 = k|1-1| - 4$
$-12 = 0 - 4$ is not true, correct transformed form is $y=k(|x-1|-4)$. Substitute $(1,-12)$:
$-12 = k(-4)$
$k = \frac{-12}{-4} = 3$

Answer:

3