Question

question 9
let ( f(x) = (x)(x - 3)(x - 6) ). what vertical stretch or compression could be applied to ( f(x) ) to make ( (1.5, 1) ) be a point on the function?

Explanation:

Step1: Define transformed function

Let the transformed function be $g(x) = k \cdot f(x)$, where $k$ is the vertical stretch/compression factor.

Step2: Calculate $f(1.5)$

First compute $f(1.5) = (1.5)(1.5-3)(1.5-6)$
$= 1.5 \times (-1.5) \times (-4.5)$
$= 1.5 \times 6.75$
$= 10.125$

Step3: Set up equation for $g(1.5)$

We know $g(1.5) = 1$, so substitute into the transformed function:
$1 = k \times 10.125$

Step4: Solve for $k$

$k = \frac{1}{10.125} = \frac{1}{\frac{81}{8}} = \frac{8}{81} \approx 0.0988$

Answer:

A vertical compression by a factor of $\frac{8}{81}$ (or approximately 0.0988) should be applied.