Answer:
The transformation from the parent function is a translation of 3 units left, a vertical stretch of scale factor 2, and a reflection in the x-axis.
Step-by-step explanation:
Given function:
[tex]\text{g}(x) = -2|x+3|[/tex]
Parent function:
[tex]\text{f}(x) = |x|[/tex]
A parent function is the simplest form of a family of functions.
The graph of g(x) is related to the graph of f(x) by a series of transformations. To determine the series of transformations, work out the steps of how to go from f(x) to g(x).
Transformations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}[/tex]
[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}[/tex]
[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}[/tex]
[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}[/tex]
[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}[/tex]
Step 1
Translation left by 3 units:
[tex]\implies f(x+3) =|x+3|[/tex]
Step 2
Stretch in the direction of the y-axis (vertically) with scale factor 2:
[tex]\implies 2f(x+3) =2|x+3|[/tex]
Step 3
Reflection in the x-axis:
[tex]\implies -2f(x+3) =-2|x+3|[/tex]
Conclusion
The transformation from the parent function is a translation of 3 units left, a vertical stretch of scale factor 2, and a reflection in the x-axis.
Learn more about graph transformations here:
https://brainly.com/question/27815602
