Question

the graph below shows a vertical compression of factor \\(\square\\) performed on the function \\(y = -|x| + 1.5\\). write the compression factor in its simplest form

Explanation:

Step1: Identify parent function vertex

Parent function $y=-|x|+1.5$ has vertex at $(0, 1.5)$.

Step2: Identify transformed vertex

From the graph, the transformed vertex is $(0, 1.5)$, and the slope of the sides is $\pm\frac{1}{2}$. For a vertical compression of $y=a(-|x|+1.5)$, the slope becomes $\pm a$.

Step3: Solve for compression factor

Set $a = \frac{1}{2}$, since the slope of the graph's lines is $\frac{1}{2}$ (from rise $\frac{1}{2}$ over run 1, or comparing to parent slope of 1).
Expression: $a = \frac{\text{Transformed Slope}}{\text{Parent Slope}} = \frac{1/2}{1} = \frac{1}{2}$

Answer:

$\frac{1}{2}$