Question

question 3
the graph below shows a vertical compression of factor
\boxed{} performed on the function $y = -|x| + 1.5$.
write the compression factor in its simplest form

Explanation:

Step1: Identify vertex of parent function

The parent function is $y = -|x| + 1.5$, its vertex is $(0, 1.5)$.

Step2: Find a point on transformed graph

From the graph, when $x=5$, $y=0$. Let the compression factor be $k$, so the transformed function is $y = -k|x| + 1.5$.

Step3: Substitute point to solve for k

Substitute $x=5$, $y=0$ into $y = -k|x| + 1.5$:
$$0 = -k|5| + 1.5$$
$$5k = 1.5$$
$$k = \frac{1.5}{5} = \frac{3}{10}$$

Answer:

$\frac{3}{10}$