Respuesta :
ANSWER
- Stretched vertically by a factor of 2
- Translated to the right 1 unit
- Reflected over the x-axis
- Translated up 2 units
EXPLANATION
We want to identify all the transformations for the given absolute value function:
[tex]f(x)=-2\lvert{x-1}\rvert+2[/tex]The parent function for absolute value functions is:
[tex]f(x)=\lvert{x}\rvert[/tex]The function was first multiplied by 2:
[tex]f(x)=2\lvert{x}\rvert[/tex]This represents a vertical stretch by a factor of 2.
Then, the function was multiplied by -1:
[tex]f(x)=-2\lvert{x}\rvert[/tex]This represents a reflection over the x-axis.
Then, the function was transformed as follows:
[tex]f(x)=-2\lvert{x-1}\rvert[/tex]This represents a horizontal translation to the right by 1 unit.
And finally, it was transformed as follows:
[tex]f(x)=-2\lvert{x-1}\rvert+2[/tex]This represents a vertical translation up by 2 units.
Hence, the transformations that the function underwent are:
- Stretched vertically by a factor of 2
- Translated to the right 1 unit
- Reflected over the x-axis
- Translated up 2 units
