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

Studdy Solution

STEP 1

Assumptions1. The original function is $f(x)=|x|+4$ . We are asked to perform a horizontal shrink by a factor of $\frac{1}{}$ on the graph of $f(x)$ 3. The transformed function will be denoted as $g(x)$

STEP 2

The horizontal shrink of a function by a factor of $\frac{1}{2}$ can be represented by replacing $x$ with $2x$ in the function. This is because when we shrink the graph horizontally, the $x$ -values get closer to the y-axis, which means they become half of their original values.So, the transformation rule is $x \rightarrow2x$ .

STEP 3

Apply the transformation rule to the original function $f(x)$ .
Replace $x$ with $2x$ in the function $f(x)$ .
$g(x) = |2(2x)|+$

STEP 4

implify the function $g(x)$ .
$g(x) = |4x|+4$ So, the function $g(x)$ that represents the graph of $f(x)$ after a horizontal shrink by a factor of $\frac{1}{2}$ is $g(x) = |4x|+4$ .

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