Answer:
Transformation of f(x) to g(x):
- Translation of 2 units right
- Vertical stretch by a factor of 2
- Translation of 1 unit up
(see attachment for graphs)
Step-by-step explanation:
Translations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\!\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
Parent function:
[tex]f(x)=x^2[/tex]
Translated 2 units to the right:
[tex]\implies f(x-2)=(x-2)^2[/tex]
Stretched vertically by a factor of 2:
[tex]\implies 2f(x-2)=2(x-2)^2[/tex]
Translated 1 unit up:
[tex]\implies 2f(x-2)+1=2(x-2)^2+1[/tex]
Therefore, the transformation of f(x) to g(x) is:
- Translation of 2 units right
- Vertical stretch by a factor of 2
- Translation of 1 unit up
Learn more about translations here:
https://brainly.com/question/27815602
