Answer:
- Translated 3 units left
- Stretched parallel to the y-axis (vertically) by a scale factor of 2
Step-by-step explanation:
Translations
For [tex]a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis by a factor of}\:a[/tex]
Parent function: [tex]f(x) = |x|[/tex]
Translated 3 units left: [tex]f(x+3)=|x+3|[/tex]
Stretched parallel to the y-axis by a factor of 2: [tex]2f(x+3)=2|x+3|[/tex]
Therefore, the function has been:
- Translated 3 units left
- Stretched parallel to the y-axis (vertically) by a scale factor of 2
Attachments
Green graph - parent function [tex]f(x) = |x|[/tex]
Red graph - Translated 3 units left [tex]f(x)=|x+3|[/tex]
Blue graph - Stretched [tex]f(x)=2|x+3|[/tex]
