QuestionFind the function $g$ that represents a vertical shrink by a factor of $\frac{1}{2}$ of $f(x)=-3|x-4|$ . $g(x)=$

Studdy Solution

STEP 1

Assumptions1. The function $f(x)=-3|x-4|$ is given. . We need to create a function $g(x)$ that represents a vertical shrink of the graph of $f(x)$ by a factor of $\frac{1}{}$ .
3. A vertical shrink by a factor of $\frac{1}{}$ means that every y-coordinate of the original function will be halved in the new function.

STEP 2

To create a function that represents a vertical shrink of the graph of $f(x)$ by a factor of $\frac{1}{2}$ , we need to multiply the function $f(x)$ by $\frac{1}{2}$ .
$g(x) = \frac{1}{2}f(x)$

STEP 3

Now, substitute the given function $f(x)=-3|x-|$ into the equation.
$g(x) = \frac{1}{2}(-3|x-|)$

STEP 4

implify the equation by distributing $\frac{1}{2}$ to $-3$ .
$g(x) = -\frac{3}{2}|x-4|$ So, the function $g(x)$ whose graph represents a vertical shrink by a factor of $\frac{1}{2}$ of the graph of $f(x)=-3|x-4|$ is $g(x)=-\frac{3}{2}|x-4|$ .

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