QuestionFind the function $g(x)$ that represents a horizontal stretch of $f(x)=|x+3|$ by a factor of 4.

Studdy Solution

STEP 1

Assumptions1. The original function is $f(x)=|x+3|$ . The transformation is a horizontal stretch by a factor of4

STEP 2

A horizontal stretch by a factor of4 means that we multiply the $x$ -values by4. In the function $f(x)=|x+|$ , the $x$ -value is inside the absolute value function, so we replace $x$ with $x/4$ in the function.
$g(x) = |x/4 +|$

STEP 3

However, we need to be careful with the arithmetic inside the absolute value function. The $+3$ inside the absolute value function should be applied after the horizontal stretch, not before. So we need to distribute the $x/$ inside the absolute value function.
$g(x) = |(x+12)/|$ So, the function $g(x)$ that represents a horizontal stretch by a factor of of the function $f(x)=|x+3|$ is $g(x) = |(x+12)/|$ .

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